Moho, seismogenesis, and rheology of the lithosphere

Tectonophysics 609 (2013) 491–503

Contents lists available at ScienceDirect

Tectonophysics journal homepage: www.elsevier.com/locate/tecto

Review Article

Moho, seismogenesis, and rheology of the lithosphere Wang-Ping Chen a, b,⁎, Chun-Quan Yu c, Tai-Lin Tseng d, Zhaohui Yang e, Chi-yuen Wang f, Jieyuan Ning g, Tiffany Leonard b a

Dept. of Ocean Science & Engineering, Zhejiang University, Hangzhou, 310058, China Dept. of Geology, University of Illinois, Urbana, IL 61801, USA Dept. of Earth, Atmospheric & Planetary Sci., Mass. Inst. of Tech., Cambridge, 02139, USA d Dept. of Geosciences, National Taiwan University, Taipei, 10617, Taiwan, ROC e Dept. of Geological Sciences, University of Colorado, Boulder, CO 80309, USA f Dept. of Earth & Planetary Science, University of California, Berkeley, CA 94720, USA g Inst. of Theoretical & Applied Geophysics, Peking University, Beijing, 100871, China b c

a r t i c l e

i n f o

a b s t r a c t

Article history: Received 22 February 2012 Received in revised form 4 September 2012 Accepted 21 December 2012 Available online 31 December 2012

The Moho is not always a sharp interface; but seismic phase SsPmp yields robust, physically averaged estimates of crustal thickness (virtual deep seismic sounding, VDSS). In S. Tibet where the Moho is as deep as 75 km, bimodal distribution of earthquake depths, with one peak in the upper crust and the other below the Moho, generated much interest in how lithological contrast affects seismicity and rheology. Generally seismicity is limited by distinct temperatures (Tc): 350±50 °C in the crust and 700±100 °C in the mantle (Earthquake Thermometry). Laboratory experiments show that distinct Tc reflect the onset of substantial crystal plasticity in major crustal and mantle minerals, respectively. Above these Tc, frictional instability ends due to velocity weakening of slip. So the seismic to aseismic transition is closely linked with brittle-ductile transitions in the crust and in the uppermost mantle, where the strength of the continental lithosphere is expected to peak (“Jelly Sandwich”). Plasticity depends exponentially on temperature (which evolves over time), so interplay between the geotherm and crustal thickness could result in concentrated seismicity in the upper crust — the only portion of a very warm lithosphere where temperature is below ~350 °C (“Crème Brûlée”). Conversely, where the entire crust is below ~350 °C (and the uppermost mantle is also below ~700 °C), then earthquakes could occur over a wide range of depths, including the entire crust and the uppermost mantle (“Caramel Slab”). © 2012 Elsevier B.V. All rights reserved.

Keywords: Earthquake focal depths Mohorovičić discontinuity Moho Mechanical instability Jelly sandwich model Caramel slab model

Contents 1. 2. 3. 4. 5.

Introduction . . . . . . . . . . . . The Moho: in the eyes of the beholder Depths of earthquakes . . . . . . . . Role of Moho in seismogenesis . . . . Emerging topics . . . . . . . . . . . 5.1. Thermal state beneath Tibet . . 5.2. Slow earthquakes and the Moho 6. Concluding remarks . . . . . . . . . Acknowledgements . . . . . . . . . . . . References . . . . . . . . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

491 492 495 496 498 498 500 501 501 501

1. Introduction

⁎ Corresponding author. E-mail address: [email protected] (W.-P. Chen). 0040-1951/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.tecto.2012.12.019

The Mohorovičić discontinuity, or the Moho, is a global feature that lies at depths between about 15 to 75 km and 5 to 10 km under the continents and the oceans, respectively (e.g., Brown and Mussett, 1993). There are only two locations where the Moho is

492

W.-P. Chen et al. / Tectonophysics 609 (2013) 491–503

exposed on the surface over large areas: the Troodos ophiolite in Cyprus and the Semail ophiolite in Oman. In both cases, relics of oceanic lithosphere overthrust onto the continent, providing rare opportunities for direct inspections (Fig. 1). These rare outcrops confirm the interpretation that the Moho is the transition between the crust and the mantle where mafic or even less magnesium- and iron-rich rocks change to ultramafic assemblages below (Brown and Mussett, 1993; Christensen and Mooney, 1995). In a well-known article, Benioff (1954) associated the cessation of deep earthquakes with the position of the Moho. In this hypothesis a seismogenic, true “mega-thrust” extends from oceanic trenches down to a depth of about 700 km where the Moho lies. While both earlier work and later research clearly showed that inclined bands of deep earthquakes occur in the interior of subducted oceanic lithosphere (Isacks and Molnar, 1969, 1971; Wadati, 1927), and that nowhere is the Moho deeper than about 75 km (e.g., Anderson, 2007; Tseng et al., 2009), the relationship between the Moho and seismogenesis has received a considerable amount of renewed attention since the discovery of unusually deep earthquakes at depths near 90 km beneath the Tibetan plateau where the thickest crust (~75 km) is found (Chen et al., 1981). The connection between the Moho and generation of earthquakes is through rheology of rocks. Since there is a marked contrast in lithology across the Moho, and lithology is an important factor in the thermomechanical properties of rocks, the Moho marks a region near where a crucial change in the instability of fault slip could occur. There is continual research on this subject (e.g., Afonso and Ranalli, 2004; Burov and Watts, 2006), including a recent review by some of the same authors (Chen et al., 2012). Here we first briefly review important means to investigate the nature of the Moho and the distribution of earthquake depths. Besides providing the necessary background information, these discussions emphasize new results or perspectives. We then connect rheology and seismogenesis in terms of slip instability, putting empirical rules of “earthquake thermometry” on firm grounds: The limiting temperatures for seismicity, Tc, are about 300–400 °C and 600–800 °C in the crust and in the upper mantle, respectively. Finally, we discuss emerging topics of current interests, including the so-called slow earthquakes and their possible relationship with the Moho and rheology. 2. The Moho: in the eyes of the beholder When Andrija Mohorovičić discovered the first major discontinuity of the Earth's interior, he relied on the method of seismic refraction. The principle of this method now widely appears in introductory texts

(e.g., Brown and Mussett, 1993): by noting the cross-over distance beyond which refracted arrival above the Moho is overtaken by refraction below the discontinuity, and by measuring the slopes of these two branches of travel-times, one can measure both the depth of the discontinuity and the speed of seismic waves above and below it. On a global scale, much of what we know about the Moho is still gathered from seismological/geophysical means. Advances in technology have revealed a wealth of information. For instance, the Moho is not always a simple interface. Deep seismic reflection has been effective in illuminating crustal structures but the Moho itself can be elusive to this particular method. Moreover, the characteristics of the Moho are quite varied; including gradual transitions between the crust and the uppermost mantle (e.g., see a recent review by Eaton (2006) and references therein). In the past two decades, it has become routine to investigate the Moho using seismic waves from distant (“teleseismic”) earthquakes. Under the general, generic name of “receiver functions” (RFs), these methods use a variety of secondary wavefields scattering off heterogeneities beneath seismic stations to investigate the subsurface. While RF cannot achieve the high frequency-content and dense spacing of conventional seismic reflection, it has several advantages: The deep-penetrating power of seismic waves generated by earthquakes is unrivaled; the broadband nature of earthquake sources facilitates multi-frequency, and therefore multi-scale studies; and the cost of deployment is modest, with minimal impact on the environment. Fig. 2a shows an example of a long seismic profile using earthquake sources. Over a distance of about 1000 km across the north China craton, wide-angle reflections off the Moho clearly reveal large variations in crustal thickness not expected from modest changes in elevation (Yu et al., 2012). The strong signal from the Moho is the so-called SsPmp phase in the coda of the S-wave train (Fig. 3b). This phase received only passing interest in the past as a useful element in RF because its amplitude is weak when the source–receiver distance is large, beyond about 55° (e.g., Owens and Zandt, 1997; Zhou et al., 2000). Lately, in order to investigate deep-seated Moho beneath thickened crust of Tibet, Tseng et al. (2009) used the large amplitude of SsPmp from earthquake sources that are between about 35°–50° away to construct deep-penetrating seismic profiles over a distance of more than 500 km over Tibet. There are two keys in this approach. First, at distances less than about 50°, the last leg of SsPmp is a post-critical reflection off the top of the Moho, resulting in amplitude of vertical ground motion that is comparable to that of the direct S-arrival, or phase Ss (Figs. 2a and 3b). Second, the “Ss” portion of the ray-paths for these two phases is near-identical (Fig. 3b). By aligning the Ss phase to the Earth's surface,

(b)

(a)

Layered Gabbronorite Harzburgite Moho (& Shear Zone) Fig. 1. Photographs of Moho outcrop in the Troodos ophiolite, Cyprus. (a) The top of the ultramafic, harzburgite massive is the “Moho”, with some serpentinization and local evidence for an extensional shear zone. (b) A clear example of layer gabbronorite (mafic crust), seen about 400 m to the right of the Moho. The length of the scale is 100 mm. (Photos taken by the first author.)

W.-P. Chen et al. / Tectonophysics 609 (2013) 491–503

493

(a)

FY05

HD01

(c)

(b)

(d) (e)

Fig. 2. Results of a deep-penetrating, P-wave reflection profile, and waveform modeling of both P- and S-wave receiver functions. (a) A virtual deep seismic sounding (VDSS) profile using the seismic phase SsPmp (see Fig. 3 for definitions) across the north China craton (NCC). Seismograms of vertical ground velocity, within the frequency-band of 0.02 and 0.5 Hz, are aligned and normalized according to the direct S-arrival, Ss. Notice the amplitude of SsPmp – wide-angle reflection off the top of the Moho – is comparable to that of the Ss phase. (b) A topographic map (in gray-scale) showing locations of seismograph stations (open triangles) and corresponding positions of reflection off the Moho for the SsPmp phase (asterisks; estimated using a nominal crustal thickness of 40 km). Two-letter codes refer to individual segments of the long seismic profile. Solid curves are boundaries of distinct geologic units within the NCC (W-, C- and E-mark the western, central and eastern NCC, respectively). Circles (in bronze) depict epicenters of large historical earthquakes (M≥6) between 1 and 2010 CE. (c) Results of waveform modeling of the S-wave train at stations HD01 and FY05 where the crust–mantle transition is sharp and very gradual, respectively. In either case, SsPmp remains clear. Observed and synthetic seismograms are plotted as solid and dashed curves, respectively. (d) P-wave counterpart of part (c), including the direct arrival, Pp, and the primary S-wave conversion, Ps. (e) Best-fitting models of P- and S-wave speeds under the two stations. (Modified from Yu et al. (2012).) See legends accompanying the figure for additional explanations.

SsPmp readily renders an image of the Moho, with the differential timing between the two phases determined by the following formula:
 2 2 1=2 T SsPmp−Ss ¼ 2H 1=V P −pβ

ð1Þ

where H is the average crustal thickness (near the station), pβ the ray-parameter (horizontal slowness) of the incident S-wave, and VP is the average P-wave speed in the crust. To put it another way, the S-P conversion point under the free surface is a virtual source for generating wide-angle reflection of the P-wave off the Moho (Fig. 3b). In this scheme of virtual deep seismic sounding (VDSS), each seismic station in an array has its own corresponding virtual source, even though there is only one physical, earthquake source. Before delving into this new approach further, it is heuristic to quickly review some often-used phases of RF that are associated with the P-wave train. The Ps phase results from the primary P-to-S conversion across the subsurface interface (Fig. 3a); and T Ps−Pp ¼ H



  2 2 1=2 2 2 1=2 1=V s –pα – 1=V p –pα

ð2Þ

where pα is the ray-parameter of the incoming P-wave, and VS the average S-wave speed in the crust. Due to small amplitude of the Ps phase, it is usually necessary to take a statistical average (“stacking”) of many RFs, each with similar source-receiver distance and back-azimuth, to enhance the signal-to-noise ratio (the reduction in random noise is proportional to the square-root of N, or the number of individual measurements). Following the same nomenclature as phases associated with the S-wave train (Fig. 3b), there are many multiples that follow the Ps phase in the P-wave train (not shown in Fig. 3a to avoid clutter). If clearly observed, arrival-times (relative to phase Pp, the direct arrival) of phases, such as PpPms, PpSms, and PsPms can be used in conjunction with TPs–Pp to estimate both H and k, the ratio between VP and Vs (e.g., Zhu and Kanamori, 2000). In this so-called H-k method, usually two constraints are available, TPs-Pp and Tmultiple-Pp. To solve for three unknowns, VP, Vs, and H (Eq. (2)), VP is generally assumed to be known. The justification comes from the fact that VP ≫Vs in the Earth, so TPs–Pp depends weakly on VP (Eq. (2); and think of the limiting case where VP approaches infinity). Notice that k is related to the Poisson's ratio, σ, as follows: h
i 2 σ ¼1=2 1–1= k −1

ð2aÞ

494

W.-P. Chen et al. / Tectonophysics 609 (2013) 491–503

Receiver Functions: Receiver-Side Scattering Virtual Source

Station

Δ

(a) Incident P-wave

p

(b) Incident

*

Surface

s

S-wave

p

s

s

P

H, crustal thickness

Moho

P

P

S

S Sp

SsPmp

Pp Ps

S Ss

Depth Phases: Source-Side Scattering

(c) Emanating

(d) Emanating

Surface

P-wave

S-wave

s p

h, focal depth

P

s P

H’, crustal thickness

S Moho

pP

s

p

*

Earthquake Source

P

sP pmP

s

*

sS

Earthquake Source

smP

S

Fig. 3. Schematic diagrams illustrating ray-paths of major seismic phases discussed in the text. For simplicity, the cases are for a single layer of crust overlying a mantle half-space — the simplest model that is sufficient for understanding the relevant principles. Notice the similarity between receiver-side (receiver functions) and source-side scattering (depth phases). In cases (a)–(c), the polarization of the S-phases is in the plane of wave propagation (“SV-component”). In case (d), the polarization is normal to the plane of wave propagation (“SH-component”). In layered, isotropic media, there is conversion/coupling only between P- and SV-components.

In the S-wave train, the phase that is equivalent to Ps is Sp, the primary S-to-P conversion across the interface (Fig. 3b); and

T Ss−Sp ¼ H



  2 2 1=2 2 2 1=2 1=V s –pβ – 1=V p –pβ

ð3Þ

Jordan and Frazer (1975) are among the first who used the Sp phase to study the Moho. Like the Ps phase, the amplitude of Sp is small, requiring either stacking of many RFs or single traces of exceptional quality (e.g., Zhou et al., 2000). An interesting feature of Sp is that is comes as a small precursor before the direct S-wave, Ss (because VP > Vs in the crust, Eq. (3)). As such, its application to investigating deep-seated interfaces is tricky, as other phases may come at about the same time and masquerade as Sp (e.g., Wilson et al., 2006). Because of the high attenuation of S-waves in the upper mantle, VDSS typically reaches frequencies of up around 0.3 Hz or so. This limit can be an advantage in that the method still constrains a physically averaged position of the Moho well, even when the Moho is a complex zone of transition. Fig. 2c–e compares results of modeling the waveforms of both P- and S-wave trains for two contrasting cases. At station HD01, distinct, single-peaked pulses for phases Ps and Sp in the P- and S-wave trains (Fig. 3a and b), respectively, indicate a sharp Moho interface and the resulting model is very simple (Fig. 2e). At station FY05, on the other hand, both phases Ps and Sp are emergent, pointing to a gradual transition from the crust to the upper mantle; and the preferred model spreads this transition over a depth of about 30 km (Fig. 2e). In this case, it would be quite misleading to define the Moho as a simple boundary. Notice that despite the transitional nature of Moho near station FY05, the SsPmp phase remains impulsive (Fig. 2c). Based on its timing relative to phase Ss, the overall crustal thickness is estimated to be about 50 km, placing the Moho, were it a simple boundary, near the middle of the crust-mantle transition. This physically averaged value of crustal thickness seems quite sensible and is particularly useful in investigating crustal contributions to isostasy or the overall

strength of the lithosphere where details of the Moho are not the primary concern. Another case in point is in central Tibet where Nowack et al. (2010) showed a complex crust–mantle transition over a horizontal distance of about 250 km. In this case, several strong scatterers, across which the impedance contrast is comparable to that across the Moho, occur between depths of 45 to 80 km. At the moment, the cause of complex or disrupted Moho is not well known. In general, exposed paleo-Moho or ultra-mafic bodies in the crust are associated with zones of continental collision (e.g., Brueckner and van Roermund, 2004; Jackson et al., 1975; Scambelluri et al., 2008; van Roermund and Drury; 1998; Vrijmoed et al., 2008). In particular, based on high resolution travel-time tomography that is multi-scale and data-adaptive (Hung et al., 2010, 2011), disrupted Moho in central Tibet is not associated with any significant anomalies in VP or Vs. Thus the incorporation of mafic or ultramafic materials into the lower crust seems to be mainly through mechanical processes, as oppose to recent magmatic activies (Chen et al., 2012; Nowack et al., 2010). At any rate, using VDSS, Tseng et al. (2009) showed that the average thickness of the crust changes quite gradually over this zone of disrupted Moho under central Tibet, shoaling from about 75 km to just over 60 km. These examples demonstrate that the VDSS is a simple, effective method that complements other forms of seismic surveys. In essence, everywhere there is a broadband seismograph within the optimal distances of about 30°–55° from earthquake sources, VDSS would yield an estimate of the average crustal thickness nearby. Such a dataset can help build regional or even global models of crustal thickness (e.g., Bassin et al., 2000; Mooney et al., 1998; http://igppweb.ucsd.edu/~gabi/ rem.html). As a final remark on VDSS, we note that in principle, the phase PpPmp in the P-wave train is akin to SsPmp. Using data from an exceptionally quite, short-period array, Tseng and Chen (2006) successfully used the PpPmp phase to image the Moho beneath the southern Indian shield. The key limitation is simply the small amplitude of PpPmp: Within the range between about 30o and 90o from earthquake sources, where

W.-P. Chen et al. / Tectonophysics 609 (2013) 491–503

complications in wave-propagation from major discontinuities in the mantle and those near the core are minimal, reflection off the Moho (the latter half of the Pmp leg of this phase) is always pre-critical and therefore of small amplitude. In comparison, the SsPmp phase exhibit large amplitude associated with post-critical reflection within the range of about 30° and 55°. 3. Depths of earthquakes In order to make a close comparison between depths of earthquakes and the Moho, we shall stay away from regions such as active zones of subduction where rapid changes in the geometry and other properties of the Moho are expected. Moreover, it is important to note that precise determination of depths of earthquakes is not a routine task; as such, focal depths reported in most earthquake catalogs and bulletins are not precise enough for the purpose here. As a general rule, unless distances between the epicenter and nearby stations are comparable to the true focal depth, travel times of direct arrivals offer little constraint on focal depth. The reason is that these arrivals have ray-paths that dive steeply downward near the source, so the vertical components of their slowness vectors are similar near the source (e.g., Menke, 1989). At regional distances, modeling of broadband waveforms, which are dominated by surface waves, does offer useful constraints on focal depth (e.g., Dreger and Helmberger, 1993). The essence of this approach comes from the fact that the level of ground motion of surface waves is frequency-dependent: the lower the frequency, the deeper the penetration. So the excitation of surface waves depends on focal depth: the deeper the earthquake, the less excited the high-frequency components (Tsai and Aki, 1970). For global studies, the most useful method for determining focal depths comes from the so-called depth phases — reflections off the free surface above the earthquakes (Fig. 3c and d). The timing of depth-phases, such as pP and sP, relative to the direct P-phase, is proportional to focal depth, h:
 2 2 1=2 T pP−P ¼ 2h 1=V’p –pα

ð4Þ

and 

  2 2 1=2 2 2 1=2 þ 1=V’p –pα T sP−P ¼ h 1=V’s –pα

ð5Þ

where pα is the ray-parameter (horizontal slowness) of the direct P-wave, and V’P and V’S are the average P- and S-wave speeds between the earthquake and the free surface, respectively. Similarly, for the S-phases:
 2 2 1=2 T sS−S ¼ 2h 1=V’s –pβ

ð6Þ

where pβ is the ray-parameter of the direct S-wave. Notice that for earthquakes shallower than about 50 km or so, depth phases could potentially interfere with the desired phases of the RF. In modern practice, both the timing and amplitude of direct- and depth-phases can be modeled with synthetic seismograms, yielding tight constraints on focal depths, fault plane solutions, and seismic moments (e.g., Langston and Helmberger, 1975; Nábelek, 1984). The first global study of the distribution of depths of intra-continental and intra-plate earthquakes was conducted almost 30 years ago (Chen and Molnar, 1983). There has been a considerable amount of additional data and new perspectives in recent years and we summarize these developments below. For the interior of the oceanic lithosphere, ruptures of many large earthquakes away from the spreading centers reach into the mantle, because the crust is only 5–10 km in thickness. Generally, the maximum depth of oceanic intra-plate earthquakes increases with the age of the

495

lithosphere and is bound by estimated positions of the 600–800 °C isotherms (Chen and Molnar, 1983; Wiens and Stein, 1983). Lately, McKenzie et al. (2005) revisited this problem. By using a revised thermal model for the oceanic lithosphere, they reported a slightly lower limiting temperature (Tc) for mantle earthquakes of about 600 °C. Thus, a Tc of about 600–800 °C seems reasonable. Interestingly, soon after the reports of Chen and Molnar (1983) and Wiens and Stein (1983), Harper (1985) used Tc to infer that the axial magma chamber episodically freezes beneath slow-spreading mid-ocean ridges, resulting in a spatially variable thermal structure that has important tectonic consequences. In particular, Harper predicted the role of low-angle detachment faults in accommodating extension, a concept which plays an increasingly important part in the modern understanding of mid-ocean ridges and the oceanic lithosphere (the so-called Chapman model, e.g., Escartín and Canale, 2011). Thermal structure of the continents is more complex than that of the oceanic lithosphere (e.g., Jaupart and Mareschal, 2011) and it is not straightforward to estimate the temperature near the source zone of the deepest intra-continental earthquakes. Nonetheless, there is a general trend that the maximum depth of earthquakes in the continental crust also increases with tectonic age (or decreasing temperature). For instance, in the North American craton, crustal earthquakes reach depths close to 30 km (Chen and Molnar, 1983). In contrast, most earthquakes in the tectonically active Tibetan plateau occur at very shallow depths of 5–10 km (Molnar and Chen, 1983), even though the crust is as thick as 75 km (Tseng et al., 2009). Lately, Behr and Platt (2011) used a combination of piezometry, thermobarometry and 2-D thermal modeling to study the history of deformation along the Whipple Mountains metamorphic core complex of the Basin and Range province. They estimated that brittle faulting in the crust ceased above a temperature of about 300 °C. This result supports earlier estimates of limiting temperature for crustal earthquakes of roughly 350±100 °C (Brace and Byerlee, 1970; Chen and Molnar, 1983). An important pattern in seismicity is the bimodal distribution of focal depths in continental regions of both active extension and contraction (Chen and Molnar, 1983; Chen and Yang; 2004; Yang and Chen, 2010). The first peak of seismicity is in the upper- to mid-crust, while the second peak occurs near the Moho at a depth of ~90 km. Based on the empirical rule that Tc of mantle earthquakes is about a factor of two greater than that of crustal seismicity, this distribution is expected for a geotherm where temperature exceeds about 350 °C in the lower crust but remains below about 700 °C in the uppermost mantle (see more discussions in the next section, especially those associated with Fig. 5). Since precise knowledge of crustal thickness is usually unavailable near the source zone of unusually deep earthquakes, some of which occurred at depths close to rough estimates of where the Moho lies, there has been some question as to whether the second peak of seismicity takes place entirely in the uppermost mantle or in the lower crust (Jackson, 2002; Maggi et al., 2000). The short answer is that there is definitely significant seismicity below the Moho. Furthermore, the second peak of seismicity always occurs near the Moho where major changes in lithology are expected (Yang and Chen, 2010). Indeed, it seems a moot point in debating whether some seismic activity can or cannot occur in the lowermost crust near the Moho, unless one knows for sure that the Moho in question is a sharp, simple discontinuity. There are two obvious ways to demonstrate that there are indeed earthquakes below the Moho. First, there are cases where the second peak of seismicity occurs at depths that exceed any reasonable expectation of how thick the crust can be. For instance, a large (mb ~ 6) earthquake, whose focal depth is conservatively estimated to be about 100 km (Chen and Yang, 2004), occurred under the westernmost Lesser Himalaya where the elevation is only about 2 km. In contrast, in all well-studied regions of the Himalayan–Tibetan orogen where the elevation exceeds 5 km, the crustal thickness ranges only from about 63

496

W.-P. Chen et al. / Tectonophysics 609 (2013) 491–503

to 75 km (e.g., Nelson et al., 1996; Tseng et al., 2009). It is difficult, if not impossible, to envisage that the crust is as thick as 100 km beneath the western Lesser Himalaya either locally or regionally. Second, under favorable conditions of having very quiet stations and impulsive earthquake sources, underside reflections off the Moho, which must be shallower than the earthquake source, have been confirmed by modeling of waveforms (Yang and Chen, 2010). These telltale signals arrive immediately after the direct P-phase and there amplitudes are small (phases pmP and smP, Fig. 3c). Nevertheless, they are observed even at individual stations without stacking of data from a close group of stations to enhance the signal-to-noise ratio (Fig. 4). Note that this approach of analysis is akin to RFs; but it takes advantage of scattered wavefield on the source side, instead of that on the receiver-side (cf. top and lower panels in Fig. 3). Interestingly, Zheng et al. (2007) used the same principle to investigate deep-seated mantle discontinuities that lie above subduction zone earthquakes.

4. Role of Moho in seismogenesis Based on results from laboratory experiments, earthquakes are associated with the so-called stick-slip phenomenon in the frictional regime of brittle deformation (e.g., see Tse and Rice, 1986 and reviews by Scholz 1990, 1998). Long intervals of “stick” corresponds to seismic quiescence of the inter-seismic stage, while sudden slips of faults result in seismic events that suddenly release stored elastic stress. Therefore a prerequisite for seismogenesis is that the source zone of earthquakes must be strong enough to accumulate elastic stress. Otherwise viscous relaxation that occurs over geologic time scales will slowly release any

(a)

buildup of stress. To this end, it is heuristic to first review how differential stress, the difference between maximum and minimum compression, is expected to vary as a function of depth in the lithosphere. Extrapolating results from experimental rock physics, over orders of magnitudes in scale and in strain rate, leads to a bimodal distribution of differential stress (“the strength-envelope”) in the continental lithosphere. In the upper crust, brittle behavior, such as frictional sliding and fracturing, dominates. These processes are very sensitive to effective pressure (the difference between ambient and pore pressure) but not to temperature, leading to a linear increase in lithospheric strength as a function of depth (Byerlee's rule, Fig. 5a): τf ¼ μρgzð1−α Þ

where τf is shear stress, μ the frictional coefficient that lies between 0.1 for clay-rich fault gouges (e.g., Carpenter et al., 2011; Chu et al., 1981; Lockner et al., 2011) and 0.6–0.8 for fresh rocks (Byerlee, 1978); ρ rock density that is generally a function of depth, z; g is gravitational acceleration; and α is the ratio between pore pressure in the rock and the lithostatic pressure. In the mid- to lower crust, increasing temperature promotes plastic micro-mechanisms such as dislocation creep that would relax the build-up of high stresses. For dislocation creep: τv ¼

 1=n   ε_ E exp A nRT

(b) INDEPTH (Stack) Δ=69.2 Az=47 o

Moho Reflections

Oct. 9, 1942

M2 M1,4

W43

M3 M5

o

Moho Reflections

P

ST18

pmP+smP pP+pwP

sP+multiples

10 s N

Moho Reflections

L. Malawi

ð8Þ

where τ v is the viscous shear stress, ε_ the strain rate, R the gas constant, T the absolute temperature, and E the activation energy (e.g.,

Event M3, Depth 44 km o o TKM2 Δ=67.6 Az=31

Rungwe

ð7Þ

ARU

KUR TKM2 MAKZ INDEPTH (Stack)

pmP+smP pP+pwP P

sP+multiples

(c)

Moho Reflections

M Fig. 4. (a) Detailed map of Lake Malawi. Solid circles represent epicenters with symbol sizes proportional to estimated fault areas. Open squares are epicenters of historical earthquakes. (b) Examples of observed (top traces of each row) and corresponding synthetic seismograms (bottom traces) for event M3 which occurred under water beneath the rift axis. Note underside reflections off the Moho (pmP) place the hypocenter some 12 km below the Moho, as evident from a differential travel-time of 2.6 ± 0.2 s between phases pmP and the direct P. Overall, long time-intervals between depths phases (pP and sP) and direct arrivals (P) constrain the focal depth to be 44 ± 4 km. Positions of observations are projections of the low hemisphere of the focal sphere and seismograms are filtered to simulate the response of the WWSSN short-period instrument. Data from station “ST18” is a single seismogram out of a stack of about 10 (“INDEPTH”). Under-side reflections off the Moho (above the earthquake source) are discernible in both cases. More data are presented by Yang and Chen (2010). (c) Another example of phase pmP from an earthquake that occurred in Zambia, about 1000 km to the west-southwest of event M3. The analog data were recorded by vertical-component, short-period instrument of the WWSSN. (Modified from Yang and Chen (2010).)

W.-P. Chen et al. / Tectonophysics 609 (2013) 491–503

Hirth and Kohlstedt, 2003; Karato, 2010). For the purpose at hand, effect of pressure is negligible, because the total range of depths involved is only on the order of 100 km. E, n and A are laboratory determined material parameters. In general, plastic mechanisms follow the Arrhenius relationship so the strength should drop exponentially with increasing temperature at depth, leading to a peak in strength near the mid-crust where the transition between brittle and plastic deformation micro-mechanisms (“brittle-ductile transition”) takes place. (To be clear, here we follow the suggestion of Evans et al. (1990) and use the term plasticity for thermally activated micromechanisms of deformation in crystals, such as dislocation creep or diffusion creep. Macroscopically, the ductile regime of rock deformation always involves plastic deformation but brittle micro-mechanisms can also accommodate part of the total strain until the transition to full plasticity is reached.) The trend of rapidly decreasing strength reverses itself near the Moho because of the major change from crustal lithology to ultramafic assemblages of the mantle, and a second peak in strength is expected in the uppermost mantle near the Moho (Fig. 5). At even greater depths, the strength of ultramafic materials diminishes at high temperature, making a gradual transition into the asthenosphere. For the ductile regime, the upper limit of stress accumulation also depends on strain rate which, for simplicity, is assumed to be constant and at steady state in Fig. 5. In general, a higher strain rate will allow more stress to accumulate in the lithosphere (e.g., see a recent review by Karato (2010) and references therein). Furthermore, strain rate may vary as a function of depth. For instance, high strain rate associated with a zone of concentrated shear in the lowermost crust will smooth out the abruptness of increase in shear stress near the Moho. Interestingly, the outcrop of oceanic Moho shown in Fig. 1, is also closely associated with a shear zone. Next, we address the link between earthquakes and the strength profile (Fig. 5). Since the mid-1980s, there has been a consensus that frictional instability can be conveniently described by a rate and state-variable (the “Dieterich–Ruina”) relationship. For our purpose, the important point to note is that the combined parameter, (a − b), is related to steady state friction, μ ss, through ss

ða–bÞ ¼ dμ =dð lnV Þ

(a)

ð9Þ

497

where V is the sliding speed, a and b are empirically determined properties of the material. More important, stability analyses showed that when (a − b) is negative (“velocity weakening”; Eq. (9)), the system is unstable, leading to sudden slips or earthquakes (e.g., Tse and Rice, 1986). Thus in addition to the buildup of elastic stress, (a − b) being negative is another necessary condition for seismogenesis; and the seismic to aseismic transition at depth corresponds to the changeover from stick-slip to stable-sliding. The connection between the seismic to aseismic transition and regimes of plastic deformation, depicted in Fig. 5, is through a strong dependence of (a −b) on temperature. Scholz (1998) showed in a review article that for granite, a material well-studied in the laboratory and abundant in the upper crust of the Earth, (a− b) is negative at low temperatures but becomes positive above about 350 °C, consistent with Tc estimated from maximum depth of intra-continental earthquakes (see Section 3). This limiting temperature for crustal seismicity is close to the onset of plasticity in quartz, the most ductile major mineral in granite (e.g., Brace and Byerlee, 1970; Scholz, 1998). In other words, through limiting temperatures, the onset of crystal plasticity greatly influenced the combined parameter (a−b); so the seismic to aseismic transition is closely linked with the brittle-ductile transition in the continental crust where the first peak in the strength profile is expected (Fig. 5a). Similarly, a limiting temperature of about 700 °C for mantle earthquakes is consistent with where (a − b) changes sign (from negative to positive at higher temperatures) for the most abundant mineral in the mantle, olivine, when experimental results by Boettcher et al. (2007) are extrapolated to geological strain rates. Therefore, following the same exact reasoning for crustal seismicity and rheology, the second, deeper peak in the strength profile (Fig. 5a) is associated with the seismic to aseismic transition in the uppermost lithospheric mantle. The saw-tooth shape of the strength envelope is sometimes referred to as the “jelly sandwich” model of rheology. A fine point to note is that after the termination of slip instability, brittle deformation probably continues for a brief interval of depth in the form of stable sliding, before plastic deformation takes over completely at the end of the brittle-ductile transition (e.g., Scholz, 1990). Thus the seismic to aseismic transition is strictly associated with the changeover from stick-slip to stable sliding. In the Earth, the

(b)

Fig. 5. (a) A schematic diagram showing how limiting values of shear stress vary with depth in the continental lithosphere (the “jelly sandwich” model). Seismogenic regions are shaded in blue while the Moho transition is hatched. Stress in the brittle regime is controlled by a linear relationship between shear and normal stresses (Byerlee's rule), while that in the plastic regime is mainly determined by distinct flow laws for crust and mantle materials (Chen and Kao, 1996; Chen and Molnar, 1983). For the latter regime, the upper limit of stress accumulation also depends on strain rate which, for simplicity, is assumed to be constant in the diagram. Data presented by Chen and Yang (2004) and Yang and Chen (2010) showed that sub-crustal earthquakes as large as magnitude 6 or greater occurred below the Moho. New modes of strain release, in the form of non-volcanic tremors and low-frequency earthquakes, also occur near the second peak of conventional earthquake activities (Ohmi et al., 2004; Shelly and Hardebeck, 2010). In comparison, the so-called “crème brûlée” model effectively places the lithosphere-asthenosphere transition above the Moho (modified from Chen et al. (2012).) (b) A schematic diagram illustrating how three hypothetical geotherms intersect with limiting temperatures for seismicity in crustal and mantle materials (step-function in orange). A high geotherm interests with the step-function only in the crust (open circle, Case 1), leading to a narrow, unimodal distribution of earthquakes in the upper crust (true, warm “crème brûlée” model). In Case 2, a moderate geotherm intersects with the earthquake thermometer three times (solid circles), resulting in a bimodal distribution of focal depths as illustrated in part (a) (“jelly sandwich” model). Finally, a very low geotherm (Case 3) does not intersect the step-function until reaching the uppermost mantle. The entire crust and the uppermost mantle are potentially seismogenic. (“caramel slab” model). The vertical scale is arbitrary in that the position of the Moho can vary between about 15 and 75 km beneath continents.

498

W.-P. Chen et al. / Tectonophysics 609 (2013) 491–503

distinction between this changeover and the brittle–ductile transition is impractical for several reasons (Chen and Kao, 1996). First, although earthquakes nucleate only under stick-slip conditions; large ruptures can continue propagating into the stable sliding domain (e.g., Scholz, 1990). Second, rupture propagation and attenuation both limit the content of high-frequency signals. So in most cases, it is impossible to determine separately the depth of nucleation and that of the centroid of the overall rupture. Third, the problem is made even more intractable due to interference from scattering near the source and the receivers (Fig. 3). For the oceanic lithosphere, the crust is so thin that it is expected to be entirely within the brittle regime; and a single peak in the strength-envelope should be in the lithospheric mantle where the brittle–ductile transition occurs. Again, using the same logic as that of the last paragraph, the distribution of shear stress as a whole is unimodal in the oceanic lithsophere, peaking near the 700 °C isotherm where seismicity terminates. In addition to temperature, strain rate, bulk composition and mineral assemblages, τ v is also dependent on grain size (for diffusion creep) and the presence of fluids or volatiles. (A vast body of work has been carried out on these topics under laboratory conditions. For instance, see summaries by Evans and Kohlstedt (1995), Hirth and Kohlstedt (2003), Karato (2010), Mackwell et al. (1998), Poirier (1995), and references therein.) The latter factor prompted some researchers to propose that a dry, mafic lower crust may be stronger than a wet, ultramafic mantle (Jackson 2002; Maggi et al., 2000). This is a variant of the so-called “crème brûlée” model which, in effect, places the bottom of the mechanical lithosphere or the top of the asthenosphere above the Moho as the bulk of the strength of the entire lithosphere is attributed to the crust. The recent review by Chen et al. (2012) discussed this issue in some detail, including perspectives from results of laboratory experiments, field observations (especially the occurrence of pseudotachylytes and large mafic boudins bound by ductile, felsic flows), numerical simulations, and the distribution of focal depths. Suffice it to say that except for regions of low geotherm where the entire crust is below about 350 °C (Chen and Molnar, 1983; Case 3 of Fig. 5b, “caramel slab”), there seems to be no clear-cut evidence for a strong, seismogenic lower crust. Moreover, geological processes that could juxtapose dry, mafic granulite over wet peridotite have not been identified (see also related discussions by Afonso and Ranalli (2004), and Burov and Watts (2006), among others). Finally, if diffusion creep is the dominant mechanism of deformation in the lithosphere, then flow laws such as Eq. (8) become linear (n = 1, or a Newtonian rheology) and τv decreases rapidly with decreasing grain size (the so-called “banana split” model, e.g., Bürgmann and Dresen (2008)). However, a Newtonian rheology is unlikely to be the controlling mechanism of deformation in the lithosphere, as seismic anisotropy, which is ubiquitous in both the crust and the lithospheric mantle, requires lattice-preferred orientation of minerals, which cannot be generated by diffusion creep (e.g., Karato, 2010). To simplify matters, we plot Tc of crustal and mantle earthquakes as a step-function of depth in Fig. 5b; and the Moho is where Tc ramps up rapidly from about 350 °C in the crust to 700 °C in the mantle. If the Moho is transitional in nature, then the step-function is more like a ramp-function near the Moho. Superimposed on this “earthquake thermometry” are three hypothetical geotherms. For a high geotherm (Case 1, Fig. 5b), temperature increases rapidly and would intersect the step-function only in the crust. In this case, earthquakes have a unimodal distribution, concentrating only in the upper- to mid-crust. In terms of the strength-envelope, strength in a weak lithosphere resides mostly in the crust; but the strong top layer of the “crème brûlée” is only skin deep, predicting a weak, aseismic lower crust. In the second case (Case 2, Fig. 5b), the modest geotherm intersects the step-function of Tc three times, first in the upper- to mid-crust, then near the Moho, and finally in the uppermost mantle. Between the first and the second intersections, temperature is higher than Tc so the distribution of seismicity is bimodal, with the Moho making the

approximate onset of the second, deeper peak in seismicity. This corresponds to the “jelly sandwich” rheology (Fig. 5a). At this juncture, it is important to point out that given the strong temperature-dependence of rheology in general and the onset of slip instability in particular, distribution of focal depths at any given tectonic setting should evolve over time and space according to how thermal structures change. Moreover, in tectonically active regions, crustal thickness also evolves over time (Chen et al., 2012). For instance, in a series of numerical simulations to gain a holistic understanding of how continental rifts evolve, Buck (1991), Hopper and Buck (1996), and Keranen et al. (2009) showed that the style of rifting seems to be tied to rheology of the continental lithosphere which, in turn, is mainly controlled by thermal state. When the geotherm is very high, neither the lower crust nor the uppermost mantle contributes much to the overall strength of a weak lithosphere. In effect, the bottom of the mechanical lithosphere is at the level of the mid-crust and the style of extension is dominated by the formation of low-angle detachments (leading to metamorphic core-complexes) in the shallow crust (Case 1, Fig. 5b). As a hot lithosphere cools, strength of the uppermost mantle becomes increasingly more important in determining the strength of the whole lithosphere, leading to wide rifts, such as the Basin and Range province of the western United States, and then eventually to narrow rift systems such as the currently active East African rift system. In other words, this model of rift evolution starts out with a modified “crème brûlée” rheology (as the lower crust is never strong) for a very hot lithosphere; as soon as the lithosphere begins cooling, it evolves into the “jelly sandwich” rheology for most of its life-cycle (Case 2, Fig. 5b). Finally, for Case 3 of Fig. 5b, the geotherm is so low that temperature intersects Tc only in the upper mantle. As such, the entire crust is strong enough to accumulate elastic stress, and the uppermost mantle would also be strong. In a very broad sense, one could view this scenario as a variant of the “crème brûlée” model; but the strong, brittle layer is thick, comprised of the entire crust as well as the uppermost mantle. So perhaps a cold “caramel slab” is an appropriate analogue. Here a broad, unimodal distribution of seismicity that straddles the Moho is expected. Such earthquakes should be very rare, because the coldest portions of the continental crust, the Archean shields, are also the most stable. In other words, temperature being below Tc is but one necessary condition for earthquakes to occur; sufficient stress is also required. One notable example of a large (mb ~ 6.4), sub-crustal earthquake did occur beneath the northern Indian shield at a depth of about 51 ± 5 km. This damaging event took place on August 20, 1988, about 25 km farther south of the Himalayan deformation front near Udayapur and its depth is well-constrained through waveform modeling/inversion (Chen and Kao, 1996). Indeed, regional data showed that background seismicity occurred throughout the crust and the uppermost mantle down to depths of about 60 km (Monsalve et al., 2006). In a recent article by Huismans and Beaumont (2011), the authors used numerical simulations to show how initial rheology affects subsequent development of rifting. Specifically, due to sufficient strength of the entire crust, a cold “caramel slab” leads to the breakup of the crust while the lithospheric mantle continues to extend plastically. Such a process offers an explanation for exposed continental lithospheric mantle on the ocean floor (e.g., along the Iberian continental margin). In contrast, for an initial “jelly sandwich” rheology, the strong lithospheric mantle breaks up first while the crust continues to extend, resulting in hyper-extended continental margins. 5. Emerging topics 5.1. Thermal state beneath Tibet With an average elevation of about 5 km over a vast area of 3 × 10 6 km 2, the Tibetan plateau is a fascinating feature on the

W.-P. Chen et al. / Tectonophysics 609 (2013) 491–503

Earth. While there is a consensus that the Himalayan–Tibetan orogen is a direct consequence of continental collision that began around 50– 55 Ma ago between Indian and Asian plates (Molnar and Tapponnier, 1975; Yin and Harrison, 2000), the thermal state beneath the most spectacular case of continental collision is a subject of on-going research (e.g., Jimenez-Munt et al., 2008). Applying earthquake thermometry to southern Tibet, where intra-continental seismicity in the mantle was first carefully demonstrated (Chen et al., 1981), leads to a curious result of a high geotherm in the upper crust overlying a low geotherm in the lithospheric mantle (Fig. 6c). Indeed there have been a number of seemingly contradicting evidences regarding the distribution of temperature beneath Tibet. In southern Tibet, available data show very high heat flows (Pollack et al., 1993), accompanied by abundant hot springs (Zheng, 1997). Strong impedance contrasts, detected in seismic reflection profiles, were interpreted as evidence for partial melting in the mid-crust (Nelson et al., 1996). In central Tibet, by associating P- and S-arrivals on seismic profiles with the α − β quartz transition (Mechie et al., 2004), estimated temperature reaches as high as 770–815 °C at

499

approximately the depth of ~32 km. All these indications point to an unusually warm upper- and mid-crust, with a high geotherm approaching 20 °C/km. Notice that the source of heat cannot be easily accounted for by magmatic activity, which has clearly shifted to northernmost Tibet since about 15 Ma ago (Chung et al., 2005). At any rate, very shallow crustal seismicity, no deeper than 10–15 km, is consistent with the notion of a warm upper/mid-crust in both southern and central Tibet (Fig. 6c) (Molnar and Chen, 1983). Meanwhile, the uppermost mantle beneath southern Tibet seems unusually cold. For instance, Pn and Sn phases, refractions in the uppermost mantle that first defined the Moho, propagate efficiently across southern Tibet at high speeds that are akin to values of cold, cratonic regions (Beghoul et al., 1993; Chen and Molnar, 1981; Liang et al., 2004; McNamara et al., 1995; Ni and Barazangi, 1983). Assuming that effect of extra pressure on wave speeds from a thickened crust is offset by that of increased temperature, Chen and Molnar (1981) estimated that the temperature of the Tibetan uppermost mantle is about 250 °C higher than that beneath shields. So according to recent estimates of geotherms for the Canadian and Indian shields (McKenzie et al., 2005;

(a)

(b)

(c)

Temperature (C)

0

500

1000

0

Depth (km)

C Moho 100

Tc (Crust)

100 (km)

M Tc (Mantle) 200

10

20

Logarithm of cumulative seismic moment; log (N m)

Fig. 6. (a) North–south trtending, vertical cross-section of VS anomalies (in fractional changes, δlnVS ) across the Himalayan–Tibetan orogen (Hung et al., 2010, 2011). IMF stands for the Indian mantle front, or the northern edge of “Greater India”. (b) Simulated temperature anomalies (relative to an average continental geotherm) beneath Tibet along the same cross-section as in (a) (Wang et al., in review). Notice the overall similarity between (a) and (b). (c) Temperature as a function of depth beneath southern Tibet where the distribution of focal depths is bimodal (inset). The step-function (in orange) shows limiting temperatures for seismicity in crustal and mantle materials, giving two constraints in temperature from focal depths (near points “C” and “M”): Shallow crustal earthquakes indicate a high geotherm in the upper crust, while mantle events specify a low temperature of only about 700 °C at a depth of approximately 100 km (dashed lines). The green curve is predicted temperature from numerical simulations by Wang et al. (in review); where the combined effect of cooling by underthrust Indian plate and viscose shear heating along the top of the Indian plate results in a temperature inversion in the now thickened lower crust of southern Tibet.

500

W.-P. Chen et al. / Tectonophysics 609 (2013) 491–503

Roy and Mareshal, 2011), the temperature just below the southern Tibetan crust is about 650 °C — a value very close to that from earthquake thermometry of mantle earthquakes there. This would imply low temperature in the upper crust, if temperature increases monotonically throughout the crust and the uppermost mantle (Fig. 6c). Taken together, a warm upper crust and a cool uppermost mantle indicate a significant change in the geothermal gradient near the mid-crust (near point C in Fig. 6c). To sustain such a change over time, the cause of high temperatures in the mid-crust must be part of the processes of on-going continental convergence. Additionally, the uppermost mantle must remain cool, in spite of the heat source that warms the upper crust. Building upon earthquake thermometry provided by a bimodal distribution of focal depths in southern Tibet and invaluable constraints from large-scale geophysical deployments such as Hi-CLIMB and INDEPTH (e.g., Chen et al., 2010; Nelson et al., 1996), we are now finally in a good position to quantitatively address the longstanding enigma of thermal state beneath Tibet. In particular, most recent results of high-resolution travel-time tomography across Tibet show conspicuous, positive anomalies of both P- and S-wave speeds (VP and VS) in the upper mantle between depths of about 100 to 250 km (Fig. 6a; Hung et al., 2010, 2011). These anomalies extend sub-horizontally, over a distance over 500 km north of the Himalayan collision front. The most straightforward interpretation of these anomalies is that they represent the advancing mantle of the underthrust Indian lithosphere, or “Greater India” (GI) (Hung et al., 2010, 2011; Priestley and McKenzie, 2006). This interpretation is supported by independent evidence, including abrupt spatial variations in shear-wave birefringence (Chen et al., 2010), and results from modeling of gravity anomalies (Jin et al., 1996). Since Archean shields are the coldest part of the continents (e.g., Jaupart and Mareschal, 2011; Jordan, 1988), underthrusting of GI brings a vast heat sink under the collision zone. Using a finite-element scheme in which all temperature-dependent properties are fully taken into account, Wang et al. (2011, in review) showed that indeed advection of the northward advancing Indian lithosphere markedly cools the collision zone as a whole, hence explaining low temperatures in the uppermost mantle of southern Tibet (Fig. 6b). Direct comparison between Fig. 6a and b shows that the overall configuration of anomalously high VS is well-explained by simulated temperature anomalies, including the gradual termination of GI near its northern terminus (IMF) due to thermal assimilation. Indeed, under central Tibet, GI has time to slowly warm up, so the uppermost mantle of central Tibet generally exceeds the Tc for earthquakes, leaving seismicity only in the upper crust (Case 1 of Fig. 5). Furthermore, the range of thermal anomalies (~ 800 K) and the corresponding fractional changes in VS (δlnVS, ~ 6%) are broadly consistent with results from laboratory experiments (e.g., Li et al., 2004). Meanwhile, viscous shear heating between the overlapping lithospheres readily accounts for a heat source that warms the upper crust. When combined with the effect of the advecting heat sink, the net result is a pronounced temperature inversion in the lower portion of now thickened Tibetan crust (Fig. 6c). In reaching this conclusion, two key processes are of particular importance. First, viscous shear heating is a self-limiting process: Increasing shear stress raises the rate of shear heating, but the resulting high temperature would exponentially reduce shear stress (Eq. (8)). Second, thermal properties are highly temperature-dependent. For instance, thermal conductivity decreases by about a factor of two between room temperature and ~1000 °C (e.g., McKenzie et al., 2005). When combined with a doubling of value in heat capacity, thermal diffusivity decreases by about a factor of four over this temperature range (McKenzie et al., 2005; Whittington et al., 2009). Thus unlike other mechanism of heating, such as a concentrated zone of radiogenic heating, high temperatures caused by shear heating tend to remain localized near the shear zone, instead of readily diffusing away from it. To

simulate these vital but complex feedback processes among temperature, thermal conductivity, and shear stress, Wang et al. (2011, in review) kept track of all temperature-dependent properties at each time-step of the numerical simulation. In Fig. 6c, the predicted peak in temperature (just above the inversion in geotherm) in the mid-crust is consistent with observations of a warm upper crust (Mechie et al., 2004; Molnar and Chen, 1983; Nelson et al., 1996; Pollack et al., 1993; Zheng, 1997), and has far-reaching implications: Such a high temperature is expected to reduce the strength of the mid-crust further than what is depicted in Fig. 5 which is appropriate for a monotonically increasing temperature with depth. An exceedingly weak layer, within the “jelly” of the “jelly sandwich” rheology profile, is expected to facilitate the continual, sub-horizontal advancement of GI toward the north. We note that channel flow of the lower crust has been proposed as a potential mechanism for bringing heat rapidly to the upper crust (e.g., Searle and Szulc, 2005). However, as noted by Hung et al. (2010, 2011), regions of anomalously low VP and VS are isolated, cylindrical features in the curst that are located along individual rifts in southern Tibet; and there is no seismic evidence for active, pervasive channel flow of the Tibetan lower crust. In any event, while a fully coupled thermo-mechanical model for Tibet is an obvious goal for further research, it is encouraging that a quantitative understanding of the link between earthquake thermometry, the Moho, and rheology seems within reach. 5.2. Slow earthquakes and the Moho In addition to ordinary earthquakes and continuous fault slip – both well-known modes of fault slip – it is now evident that fault slip can occur over a wide range of characteristic time-scales. The new modes of fault slip bear many different names and there is no consensus on mechanisms that control this wide array of behaviors. What seems clear is that for a given seismic moment, such new modes of slip have characteristic durations that are greater than conventional earthquakes (Ide et al., 2007 and references therein). (The seismic moment M, is a true measure of the size of a slip event, defined by the product of the slip area (A), the amount of slip (D) and the shear modulus of the source region (μ) (Aki and Richards, 2002). Chen et al. (2012) proposed that the term be generalized to “slip moment”.) Ide et al. (2007) collectively referred to unconventional slip events as “slow earthquakes”. While the difference between conventional and slow earthquakes seems convincing, data for non-traditional earthquakes are limited; making it unclear if all slow events follow a single scaling rule. Most of these new models of strain release occur along or near the plate interface at subduction zones (e.g., Vidale and Houston, 2012) where significant vertical motions across the plate boundary make it difficult to investigate the role of Moho. A notable exception is the segment of the San Andreas transform fault system near Parkfield, California where strike-slip motion dominates. Nadeau and Dolenc (2005) reported tectonic (non-volcanic) tremors – low amplitude but long-lasting vibrations – in the Parkfield area. Recently, Shelly and Hardebeck (2010 and references therein) showed that these tectonic tremors appear to be comprised of numerous overlapping low-frequency earthquakes: events with distinct P- and S-wave arrivals but whose frequency-content is only slightly lower than ordinary earthquakes of comparable slip moments. One of the most important observations is that the tremor “families” (clusters) all occurred between depths of about 18 to 30 km, significantly below the zone of ordinary micro-earthquakes and the slip zone during the 2004 Parkfield earthquake which concentrates above depths of 10 to 15 km in the upper crust. Shelly and Hardebeck (2010) inferred that all tremor families are in the lowermost crust. However, precise position of the Moho is not known along this section of the San Andreas fault (see Chen et al. (2012) for detailed discussions and references). Given the

W.-P. Chen et al. / Tectonophysics 609 (2013) 491–503

range of about 10 km in the depths of such events and uncertainties in estimated positions of the Moho, many tremors occurred very close to the Moho and some of them may have occurred in the uppermost mantle, resembling the position of the second peak of seismicity already discussed (Fig. 5a). Another example of these patterns along strike-slip fault zones is associated with the western Tottori earthquake of 2000 in southwestern Japan where the position of the Moho near the source region is unknown (Ohmi et al., 2004). In this case, both the main shock and most aftershocks occur in the top 12 km of the crust. A number of low-frequency earthquakes occurred between depths of 25 and 35 km both prior to and after the main shock, leaving a conspicuous, aseismic gap between depths of 12 to 25 km. At this juncture, the dynamics of slow earthquakes and physical conditions that govern their genesis are not known and are targets of intense research (e.g., Shelly, 2010a,b; Vidale and Houston, 2012). Nonetheless, such events do release seismic radiation and therefore require some degree of elastic strain accumulation. In order to address the issue of whether the gap in seismic radiation near Parkfield and Tottori is a minimum in crustal strength where little or no elastic stress can accumulate (Fig. 5a), precise knowledge of the geometry and properties of the Moho surrounding these areas is urgently needed.

501

“caramel slab” model. On the other extreme, when temperatures exceed about 350 °C except in the upper crust, only shallow, crustal earthquake are expected (e.g., Molnar and Chen, 1983; Yang and Chen, 2010) – the warm “crème brûlée” model. Recent, high resolution results regarding the configuration of overlapping lithospheres under the Himalayan–Tibetan orogeny (Hung et al., 2010, 2011; Priestley and McKenzie, 2006), when combined with constraints on temperature from earthquake thermometry, facilitate a quantitative understanding of a warm upper crust overlying a cool uppermost mantle in southern Tibet. In a nutshell, numerical simulations that take full account of 1) temperature dependent properties such as thermal conductivity and heat capacity, and 2) complex feedbacks amongst temperature, shear stress and the rate of viscous shear heating, show a temperature inversion in the lower crust. This result is the combined effect of an advecting heat sink, the underthrusting Indian plate, and viscous shear heating along overlapping lithospheres (Wang et al., 2011, in review). Finally, even in important geological regions such as the San Andreas fault system near Parkfield, uncertainties about the configuration of the Moho are still too large to properly address the link among slow earthquakes, regular seismicity, the Moho, and rheology. To this end, new ways of illuminating the subsurface, such as the VDSS, hold the promise of a true global understanding the Moho and its role in seismogenesis.

6. Concluding remarks After one hundred years of research, building a global model of the crust is still an on-going endeavor. Current efforts that rely on seismic refraction/reflection surveys extrapolate from a limited geographic coverage (e.g., Crust 5.1; Mooney et al., 1998), while those that incorporate surface waves for expansive coverage have limitations in vertical resolution (e.g., Bassin et al., 2000; Crust 2.0; http://igppweb.ucsd.edu/ ~gabi/rem.html). In addition, receiver functions contribute to this effort (e.g., Zandt and Ammon, 1995), but so far the best constraints only come from permanent, broadband stations because the most commonly used phase, Ps, is quite small and requires stacking of data from many earthquake sources. To this end, deep-penetrating, virtual seismic sounding (VDSS) using the SsPmp phase shows great promise in that its strong signal requires only one suitable earthquake to illuminate the Moho beneath every station of a portable array (Fig. 2; Tseng et al., 2009; Yu et al., 2012). In continental regions currently under either contraction or extension, a bimodal distribution of focal depths, with peaks concentrating in the upper crust and below the Moho, is now firmly established, supporting the “jelly sandwich” rheology of continental lithosphere (e.g., Chen and Molnar, 1983; Chen and Yang, 2004; Yang and Chen, 2010). Equally important is that several pieces of evidence show that large earthquakes do occur in the mantle under continental crust (Chen and Yang, 2004; Yang and Chen, 2010). Rheology of the lithosphere depends on many factors, including temperature, pressure, strain rate, bulk composition and mineral assemblages, grain size, and the presence of fluids or volatiles. Meanwhile, a number of studies show that earthquake occurrences are limited by distinct temperatures (Tc): 300–400 °C for crustal earthquakes and 600–800 °C for earthquakes in the mantle. These empirical rules are now corroborated by laboratory experiments, linking the onset of crystal plasticity of major minerals to the cessation of frictional instability at high temperatures (Boettcher et al., 2007; Scholz, 1998). The change in Tc occurs across the Moho where ultramafic rocks of the upper mantle turn into less iron/magnesium rich assemblages of the crust. Since temperature must evolve over geologic time, the appropriate rheology model, and its manifestation in the distribution of focal depths for any particular region can be understood as the interplay among the geotherm, the average crustal thickness, and the Tc. When the entire crust and the uppermost mantle are cooler than about 700 °C, earthquakes are expected to occur from near the surface to the uppermost mantle (e.g., Chen and Kao, 1996; Monsalve et al., 2006) – the cold

Acknowledgements We thank discussions with G. Hirth and S. Karato over the years. Reviews by J.C. Afonso and an anonymous reviewer help improve the original manuscript. Chen thanks Shell Oil for subsidizing a field course during which he made Gigapan images, a mosaic of hundreds of high-resolution photographs, of the Moho outcrop in Cyprus (https://uofi.box.com/pubs and click on the file named GigaPanLinks. txt). The 2011 CIDER (Cooperative Institute for Dynamic Earth Research; under US NSF grant EAR 09-68979) summer program brought Wang and Chen together for this collaboration. This research was supported by Zhejiang University through grants from the Chinese Ministry of Education (“985”), and by US NSF grants EAR-99-09362 (Hi-CLIMB), EAR05-51995, and EAR06-35419. Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect those of the NSF. References Afonso, J.C., Ranalli, G., 2004. Crustal and mantle strengths in continental lithosphere: is the jelly sandwich model obsolete? Tectonophysics 394, 221–232. Aki, K., Richards, P.G., 2002. Quantitative seismology. Univ. Sci. Books, Sausalito, CA (704 pp.). Anderson, D.L., 2007. New theory of the Earth. Cambridge Univ. Press, New York (384 pp.). Bassin, C., Laske, G., Masters, T.G., 2000. The current limits of resolution for surface wave tomography in North America. EOS. Transactions of the American Geophysical Union 81, F897. Beghoul, N., Barazangi, M., Isacks, B., 1993. Lithospheric structure of Tibet and western North America: Mechanisms of uplift and a comparative study. Journal of Geophysical Research 98, 1997–2016. Behr, W.M., Platt, J.P., 2011. A naturally constrained stress profile through the middle crust in an extensional terrane. Earth and Planetary Science Letters 303, 181–192. Benioff, H., 1954. Orogenesis and deep crustal structure: Additional evidence from seismology. Geological Society of America Bulletin 65, 385–400. Boettcher, M.S., Hirth, G., Evans, B., 2007. Olivine friction at the base of oceanic seismogenic zones. Journal of Geophysical Research 112 (B01205). http:// dx.doi.org/10.1029/2006JB004301. Brace, W.F., Byerlee, J.D., 1970. California earthquakes: Why only shallow focus? Science 168, 1573–1576. Brown, A.E., Mussett, G.C., 1993. The inaccessible Earth. Chapman and Hall (276 pp.). Brueckner, H.K., van Roermund, H.L.M., 2004. Dunk Tectonics: a multiple subduction/ eduction model for the evolution of the Scandianvian Caledonides. Tectonics 23 (TC2004). http://dx.doi.org/10.1029/2003TC001502. Buck, W.R., 1991. Modes of continental lithospheric extension. Journal of Geophysical Research 96 (B12), 20,161–20,178. Bürgmann, R., Dresen, G., 2008. Rheology of lower crust and upper mantle: Evidence from rock mechanics, geodesy, and field observations. Annual Review of Earth and Planetary Sciences 36, 531–567.

502

W.-P. Chen et al. / Tectonophysics 609 (2013) 491–503

Burov, E., Watts, A.B., 2006. The long-term strength of continental lithosphere: "jelly sandwich" or "crème brûlée". GSA Today 16 (1). http://dx.doi.org/10.1130/1052-5173. Byerlee, J., 1978. Friction of rocks. Pure and Applied Geophysics 116, 615–626. Carpenter, B.M., Marone, C., Saffer, D.M., 2011. Weakness of the San Andreas fault revealed by samples from the active fault zone. Nature Geoscience 4, 251–254. http://dx.doi.org/10.1038/NGEO1089. Chen, W.-P., Kao, H., 1996. Seismotectonics of Asia: Some recent progress. In: Yin, A., Harrison, M. (Eds.), The Tectonic Evolution of Asia. Cambridge Univ. Press, Palo Alto, pp. 37–62. Chen, W.-P., Molnar, P., 1981. Constraints on seismic wave velocity structure beneath the Tibetan plateau and their tectonic implications. Journal of Geophysical Research 86, 5937–5962. Chen, W.-P., Molnar, P., 1983. Focal depths of intracontinental and intraplate earthquakes and their implications for the thermal and mechanical properties of the lithosphere. Journal of Geophysical Research 88, 4183–4214. Chen, W.-P., Yang, Z.-H., 2004. Earthquakes beneath the Himalayas and Tibet: Evidence for strong lithospheric mantle. Science 304, 1949–1952. Chen, W.-P., Nábelek, J.L., Fitch, T.J., Molnar, P., 1981. An intermediate depth earthquake beneath Tibet: source characteristics of the event of September 14, 1976. Journal of Geophysical Research 86, 2863–2876. Chen, W.-P., et al., 2010. Shear-wave birefringence and current configuration of converging lithosphere under Tibet. Earth and Planetary Science Letters 295 (1–2), 297–304. http://dx.doi.org/10.1016/j.epsl.2010.04.017. Chen, W.-P., et al., 2012. Rheology of the continental lithosphere: Progress and new perspectives. Gondwana Research 21, 4–18. http://dx.doi.org/10.1016/j.gr.2011.07.013. Christensen, N.I., Mooney, W.D., 1995. Seismic velocity structure and composition of the continental crust: A global view. Journal of Geophysical Research 100, 9761–9788. Chu, C.-L., Wang, C.-Y., Lin, W., 1981. Permeability and frictional properties of San Andreas fault gouges. Geophysical Research Letters 8, 565–568. http://dx.doi.org/ 10.1029/GL008i006p00565. Chung, S.-L., et al., 2005. Tibetan tectonic evolution inferred from spatial and temporal variations in post-collisional magmatism. Earth-Science Reviews 68, 173–196. Dreger, D.S., Helmberger, D.V., 1993. Determination of source parameters at regional distances with three-component sparse network data. Journal of Geophysical Research 98, 8107–8125. Eaton, D.W., 2006. Multi-genetic origin of the continental Moho: insights from Lithoprobe. Terra Nova 18 (1), 34–43. Escartín, J., Canale, J.P., 2011. Detachments in oceanic lithosphere: Deformation, magmatism, fluid flow and ecosystems. EOS. Transactions of the American Geophysical Union 92 (4), 31–32. Evans, B., Kohlstedt, D.L., 1995. Rheology of rocks. American Geophysical Union Reference Shelf 3, 148–165. Evans, B., Fredrich, J.T., Wong, T.-f., 1990. The brittle to ductile transition in rocks: Recent experimental and theoretical progress. Geophysical Monograph 56, 1–20. Harper, G.D., 1985. Tectonics of slow spreading mid-ocean ridges and consequences of a variable depth to the brittle/ductile transition. Tectonics 4 (4), 395–409. Hirth, G., Kohlstedt, D.L., 2003. Rheology of the upper mantle and the mantle wedge: A view from the experimentalists. Geophysical Monograph 138, 83–105. Hopper, J., Buck, W.R., 1996. The effect of lower crustal flow on continental extension and passive margin formation. Journal of Geophysical Research 101 (B9), 20,175–20,194. Huismans, R., Beaumont, C., 2011. Depth-dependent extension, two-stage breakup and cratonic underplating at rifted margins. Nature 473, 74–78. Hung, S.-H., Chen, W.-P., Chiao, L.-Y., Tseng, T.-L., 2010. First multi-scale, finitefrequency tomography illuminates 3-D anatomy of the Tibetan plateau. Geophysical Research Letters 37. http://dx.doi.org/10.1029/2009GL041875. Hung, S.-H., Chen, W.-P., Chiao, L.-Y., 2011. A data-adaptive, multi-scale approach of finite-frequency, travel-time tomography with special reference to P- and Swave data from central Tibet. Journal of Geophysical Research 116, B06307. http://dx.doi.org/10.1029/2010JB008190. Ide, S., Beroza, G.C., Shelly, D.R., Uchide, T., 2007. A scaling law for slow earthquakes. Nature 447, 76–79. Isacks, B., Molnar, P., 1969. Mantle earthquake mechanisms and the sinking of the lithosphere. Nature 233, 1121–1124. Isacks, B., Molnar, P., 1971. Distribution of stresses in the descending lithosphere from a global survey of focal-mechanism solutions of mantle earthquakes. Reviews of Geophysics 9, 103–174. Jackson, J., 2002. Strength of the continental lithosphere: Time to abandon the jelly sandwich? GSA Today 12, 4–10. Jackson, E.D., Green, H.W., Moores, E.M., 1975. The Vourinos ophiolite, Greece: Cyclic units of lineated cumulates overlying harzburgite tectonite. Geological Society of America Bulletin 86, 390–398. Jaupart, C., Mareschal, J.-C., 2011. Heat generation and transport in the Earth. Cambridge Univ. Press, Cambridge (464 pp.). Jimenez-Munt, I., Fernandez, M., Verges, J., Platt, J.P., 2008. Lithosphere structure underneath the Tibetan plateau inferred from elevation, gravity and geoid anomalies. Earth and Planetary Science Letters 267 (1–2), 276–289. http://dx.doi.org/ 10.1016/j.epsl.20078.11.045. Jin, Y., McNutt, M.K., Zhu, Y.-S., 1996. Mapping the descent of Indian and Eurasian plates beneath the Tibetan plateau from gravity anomalies. Journal of Geophysical Research 101, 11,275–11,290. Jordan, T.H., 1988. Structure and formation of the continental tectosphere. Journal of Petrology, Special Lithosphere Issue 11–37. Jordan, T.H., Frazer, L.N., 1975. Crustal and upper mantle structure from Sp phases. Journal of Geophysical Research 80, 1504–1518. Karato, S.-I., 2010. Rheology of the Earth's mantle: A historical review. Gondwana Research 18, 17–45.

Keranen, K.M., Klemperer, S.L., Julia, J., Lawrence, J.F., Nyblade, A.A., 2009. Low lower crustal velocity across Ethiopia: Is the Main Ethiopian Rift a narrow rift in a hot craton? Geochemistry, Geophysics, Geosystems 10, Q0AB01. http://dx.doi.org/ 10.1029/2008GC002293. Langston, C.A., Helmberger, D.V., 1975. A proceedure for modeling shallow dislocation sources. Geophysical Journal of the Royal Astronomical Society 42, 117–130. Li, B., Kung, J., Liebermann, R.C., 2004. Modern techniques in measuring elasticity of Earth materials at high pressure and high temperature using ultrasonic interferometry in conjunction with synchrotron X-radiation in multi-anvil apparatus. Physics of the Earth and Planetary Interiors 143–144, 559–574. Liang, C., Song, X., Huang, J.L., 2004. Tomographic inversion of Pn travel times in China. Journal of Geophysical Research 109 (B11304). http://dx.doi.org/10.1029/ 2003JB002789. Lockner, D.A., Morrow, C., Moore, D., Hickman, S., 2011. Low strength of deep San Andreas fault gouge from SAFOD core. Nature 472, 82–85. http://dx.doi.org/10.1038/ nature09927. Mackwell, S.J., Zimmerman, M.E., Kohlstedt, D.L., 1998. High-temperature deformation of dry diabase with application to tectonics of Venus. Journal of Geophysical Research 103, 975–984. Maggi, A., Jackson, J.A., McKenzie, D., Priestley, K., 2000. Earthquake focal depths, effective elastic thickness, and the strength of the continental lithosphere. Geology 28, 495–498. McKenzie, D., Jackson, J., Priestley, K., 2005. Thermal structure of oceanic and continental lithosphere. Earth and Planetary Science Letters 233, 337–349. McNamara, D.E., Owens, T.J., Walter, W.R., 1995. Observations of regional phase propagation across the Tibetan plateau. Journal of Geophysical Research 100, 22,215–22,229. Mechie, J., et al., 2004. Precise temperature estimation in the Tibetan crust from seismic detection of the α−β quartz transition. Geology 32, 601–604. http://dx.doi.org/ 10.1130/G20367.1. Menke, W., 1989. Geophysical data analysis: Discrete inverse theory. Academic Press, New York (289 pp.). Molnar, P., Chen, W.-P., 1983. Depths and fault plane solutions of earthquakes under the Tibetan plateau. Journal of Geophysical Research 88, 1180–1196. Molnar, P., Tapponnier, P., 1975. Cenozoic tectonics of Asia: Effects of a continental collision. Science 189, 419–426. Monsalve, G., et al., 2006. Seismicity and one-dimentional velocity structure of the Himalayan collision zone; earthquakes in the crust and upper mantle. Journal of Geophysical Research 111 (B10). http://dx.doi.org/10.1029/2005JB004062. Mooney, W.D., Laske, G., Masters, T.G., 1998. CRUST 5.1: A global crustal model at 5° x 5°. Journal of Geophysical Research 103, 727–747. Nábelek, J.L., 1984. Determination of earthquake source parameters from inversion of body waves. Ph.D. Thesis, Mass. Inst. of Technol., Cambridge, MA. Nadeau, R.M., Dolenc, D., 2005. Nonvolcanic tremors deep beneath the San Andreas Fault. Science 307, 389. http://dx.doi.org/10.1126/science.1107142. Nelson, K.D., et al., 1996. Partially molten middle crust beneath southern Tibet: Synthesis of project INDEPTH results. Science 274, 1684–1688. Ni, J., Barazangi, M., 1983. High-frequency seismic wave propagation beneath the Indian shield, Himalaya arc, Tibetan plateau and surrounding regions: High uppermost mantle velocities and efficient propagation beneath Tibet. Geophysical Journal of the Royal Astronomical Society 72, 665–689. Nowack, R.L., Chen, W.-P., Tseng, T.-L., 2010. Application of Gaussian beam migration to multi-scale imaging of the lithosphere beneath the Hi-CLIMB array in Tibet. Bulletin of the Seismological Society of America 100, 1743–1754. Ohmi, S., Hirose, I., Mori, J.J., 2004. Deep low-frequency earthquakes near the downward extension of the seismogenic fault of the 2000 Western Tottori earthquake. Earth, Planets and Space 56, 1185–1189. Owens, T.J., Zandt, G., 1997. Implications of crustal property variations for models of Tibetan plateau evolution. Nature 387, 37–43. Poirier, J.-P., 1995. Plastic rheology of crystals. American Geophysical Union Reference Shelf 2, 237–247. Pollack, H.N., Hurter, S.J., Johnson, J.R., 1993. Heat flow from the Earth's interior: Analysis of the global data set. Reviews of Geophysics 31, 267–280. http://dx.doi.org/ 10.1029/93RG01249. Priestley, K., McKenzie, D., 2006. The thermal structure of the lithosphere from shear wave velocities. Earth and Planetary Science Letters 244, 285–301. http:// dx.doi.org/10.1016/j.epsl.2006.01.008. Roy, S., Mareshal, J.-C., 2011. Constraints on the deep thermal structure of the Dharwar craton, India, from heat flow, shear wave velocities, and mantle xenoliths. Journal of Geophysical Research 116 (B02409). http://dx.doi.org/10.1029/2010JB007796. Scambelluri, M., Petke, T., van Roermund, H.L.M., 2008. Majoritic garnets monitor deep subduction fluid flow and mantle dynamics. Geology 36, 59–62. Scholz, C.H., 1990. Mechanics of earthquakes and faulting. Cambridge Univ. Press, Cambridge (439 pp.). Scholz, C.H., 1998. Earthquakes and friction laws. Nature 391, 37–42. Searle, M.P., Szulc, A.G., 2005. Channel flow and ductile extrusion of the high himalayan slab-the Kangchenjunga-Darjeeling profile, Sikkim Himalaya. Journal of Asian Earth Sciences 25 (1), 173–185. Shelly, D.R., 2010a. Migrating tremors illuminate complex deformation beneath the seismogenic San Andreas fault. Nature 463, 648–653. http://dx.doi.org/10.1038/ nature08755. Shelly, D.R., 2010b. Periodic, chaotic, and doubled earthquake recurrence Intervals on the deep San Andreas fault. Science 328, 1385–1388. http://dx.doi.org/10.1126/ science.1189741. Shelly, D.R., Hardebeck, J.L., 2010. Precise tremor source locations and amplitude variations along the lower-crustal central San Andreas Fault. Geophysical Research Letters 37 (L14301). http://dx.doi.org/10.1029/2010GL043672.

W.-P. Chen et al. / Tectonophysics 609 (2013) 491–503 Tsai, Y.B., Aki, K., 1970. Precise focal depth determination from amplitude spectra of surface waves. Journal of Geophysical Research 75, 5729–5743. Tse, S.T., Rice, J.R., 1986. Crustal earthquake instability in relation to the depth variation of frictional slip properties. Journal of Geophysical Research 91, 9452–9472. Tseng, T.-L., Chen, W.-P., 2006. Probing the southern Indian shield with P-wave receiverfunction profiles. Bulletin of the Seismological Society of America 96, 328–333. Tseng, T.-L., Chen, W.-P., Nowack, R.L., 2009. Northward thinning of Tibetan crust revealed by virtual seismic profiles. Geophysical Research Letters 36, L24304. http://dx.doi.org/10.1029/2009GL040457. van Roermund, H.L.M., Drury, M.R., 1998. Ultra-high pressure (P > 6 GPa) garnet peridotites in western Norway: Exhumation of mantle rocks from >185 km depth. Terra Nova 10, 295–301. Vidale, J.E., Houston, H., 2012. Slow slip: A new kind of earthquake. Physics Today 65 (1), 38–43. http://dx.doi.org/10.1063/PT.3.1399. Vrijmoed, J.C., Smith, D.C., van Roermund, H.L.M., 2008. Raman confirmation of microdiamond in the Svartberget Fe-Ti type garnet-peridotite, Western Gneiss Region, Norway. Terra Nova 20, 295–301. Wadati, K., 1927. Existence and study of deep-focus earthquakes (in Japanese). Journal of the Meteorological Society of Japan Ser. 2 (5), 119–145. Wang, C.-Y., Chen, W.-P., Wang, L.-P., 2011. Is Tibetan crust hot? (Abstract). EOS. Transactions of the American Geophysical Union 92 (FM T51J-02). Wang, C.-Y., Chen, W.-P., Wang, L.-P., in review. Temperature beneath Tibet. Earth and Planetary Science Letters. Whittington, A.G., Hofmeister, A.M., Nabelek, P.I., 2009. Temperature-dependent thermal diffusivity of the Earth's crust and implications for magmatism. Nature 459, 319–321. http://dx.doi.org/10.1038/nature07818.

503

Wiens, D.A., Stein, S., 1983. Age dependence of oceanic intraplate seismicity and implications for lithospheric evolution. Journal of Geophysical Research 88, 6455–6468. Wilson, D., Angus, D., Ni, J., Grand, S., 2006. Constraints on the interpretation of S-to-P receiver functions. Geophysical Journal International 165, 969–980. Yang, Z.-H., Chen, W.-P., 2010. Earthquakes along the East African Rift System: A system-wide, multi-scale perspective. Journal of Geophysical Research 115, B12309. http://dx.doi.org/10.1029/2009JB006779. Yin, A., Harrison, T.M., 2000. Geologic evolution of the Himalayan-Tibetan orogen. Annual Review of Earth and Planetary Sciences 28, 211–280. Yu, C.-Q., et al., 2012. Thick crust beneath the Ordos Plateau: Implications for instability of the North China Craton. Earth Planetary Science Letters 357–358, 366–375. http://dx.doi.org/10.1016/j.epsl.2012.09.027. Zandt, G., Ammon, C.J., 1995. Continental crust composition constrained by measurements of crustal Poisson's ratio. Nature 374, 152–154. Zheng, M., 1997. Introduction to saline lakes on the Qinghai-Tibet plateau. Kluwer Academic Publishers, Dordrecht, Netherlands (328 pp.). Zheng, Y., Lay, T., Flanagan, M.P., Williams, Q., 2007. Pervasive seismic wave reflectivity and metasomatism of the Tonga mantle wedge. Science 316 (5826), 855–859. Zhou, L.-M., Chen, W.-P., Özalaybey, S., 2000. Seismic properties of the central Indian shield from broadband P-SV conversions at Hyderabad. Bulletin of the Seismological Society of America 90, 1295–1304. Zhu, L., Kanamori, H., 2000. Moho depth variation in Southern California from teleseismic receiver functions. Journal of Geophysical Research 105, 2969–2980.