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Volume 28 Issue 1
Feb.  2017
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Yixian Xu, Lupei Zhu, Qinyan Wang, Yinhe Luo, Jianghai Xia. Heat Shielding Effects in the Earth’s Crust. Journal of Earth Science, 2017, 28(1): 161-167. doi: 10.1007/s12583-017-0744-6
Citation: Yixian Xu, Lupei Zhu, Qinyan Wang, Yinhe Luo, Jianghai Xia. Heat Shielding Effects in the Earth’s Crust. Journal of Earth Science, 2017, 28(1): 161-167. doi: 10.1007/s12583-017-0744-6

Heat Shielding Effects in the Earth’s Crust

doi: 10.1007/s12583-017-0744-6
More Information
  • Knowledge of heat flow and associated variations of temperature with depth is crucial for understanding how the Earth functions. Here, we demonstrate possible heat shielding effects that result from the occurrence of mafic intrusions/layers (granulitic rocks) within a dominantly granitic middle crust and/or ultramafic intrusions/layers (peridotitic rocks) within a dominantly granulitic lower crust; heat shielding is a familiar phenomenon in heat engineering and thermal metamaterials. Simple one-dimensional calculations suggest that heat shielding due to the intercalation of granitic, granulitic and peridotitic rocks will increase Moho temperatures substantially. This study may lead to a rethinking of numerous proposed lower crustal processes.
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Heat Shielding Effects in the Earth’s Crust

doi: 10.1007/s12583-017-0744-6

Abstract: Knowledge of heat flow and associated variations of temperature with depth is crucial for understanding how the Earth functions. Here, we demonstrate possible heat shielding effects that result from the occurrence of mafic intrusions/layers (granulitic rocks) within a dominantly granitic middle crust and/or ultramafic intrusions/layers (peridotitic rocks) within a dominantly granulitic lower crust; heat shielding is a familiar phenomenon in heat engineering and thermal metamaterials. Simple one-dimensional calculations suggest that heat shielding due to the intercalation of granitic, granulitic and peridotitic rocks will increase Moho temperatures substantially. This study may lead to a rethinking of numerous proposed lower crustal processes.

Yixian Xu, Lupei Zhu, Qinyan Wang, Yinhe Luo, Jianghai Xia. Heat Shielding Effects in the Earth’s Crust. Journal of Earth Science, 2017, 28(1): 161-167. doi: 10.1007/s12583-017-0744-6
Citation: Yixian Xu, Lupei Zhu, Qinyan Wang, Yinhe Luo, Jianghai Xia. Heat Shielding Effects in the Earth’s Crust. Journal of Earth Science, 2017, 28(1): 161-167. doi: 10.1007/s12583-017-0744-6
  • The Moho beneath many tectonically young areas probably lies within a complex transition zone of intercalated granulitic and peridotitic rocks (O'Reilly and Griffin, 2013). Evidence for this assertion is the distribution of xenoliths that originate from different parts of the crust and uppermost mantle and the strongly layered subhorizontal seismic reflectors near the Moho (e.g., Thybo and Nielsen, 2009) that are best explained by models comprising of alternating layers of high and low P-wave velocity (e.g., Teng et al., 2013; O'Reilly et al., 2010; Hale and Thompson, 1982). Furthermore, mafic (i.e., granulitic) intrusions into the generally granitic middle crust and multiple shear zones near the transition between the brittle upper crust and ductile lower crust are responsible for layered subhorizontal reflections in seismic data sets worldwide, e.g., Lake Bullen Merri area of southeastern Australia (Finlayson et al., 1993), South Tibet (Nelson et al., 1996), the Dabie-Sulu orogenic belt (Yang, 2009; Yuan et al., 2003) and many other regions. Coincident significance of seismic anisotropy (Luo et al., 2013), high S-wave velocities (Luo et al., 2012) and layered reflectors (Yuan et al., 2003) in the middle crust of the Dabie-Sulu orogen are indicative of macro-anisotropy (e.g., Carcione et al., 1991) due to alternating thin layers of granitic and granulitic rocks. Different heat productivities and thermal conductivities are undoubtedly associated with the different lithologies (Jaupart and Mareschal, 2007) which may result in a remarkable shielding effect similar to heat flux manipulation (Narayana and Sato, 2012). And furthermore thermal conductivity may be intrinsic anisotropy, for example, the thermal conductivity of gneiss perpendicular to foliation is only 60% percent of that parallel to foliation (Jaupart and Mareschal, 2007).

    A wide variety of proposed lower crust processes, e.g., magma mixing (Petford et al., 2000), continental overflow (Bailey, 1999), ductile flow (Searle, 2013) and channel flow (Royden et al., 1997) require much higher temperatures than commonly assumed. Lower crustal or lithospheric delamination and subsequent mantle upwelling or underplating (Thybo and Artemieva, 2013; Stratford and Thybo, 2011; Bergantz, 1989; Bird, 1979; and references therein) are currently the most popular explanations for elevated temperatures in the lower crust. However, there are only a few convincing examples of seismically imaged delaminated slabs in the deep upper mantle, even in tectonically very young areas.

    Here an alternative approach is proposed to explain for the elevated temperature in the Earth's crust, which is taken into account of the crustal structure resulted from different lithofacies. This mechanism can be one of reasons for partial melting occurred in middle-to-lower crust, and a suitable model especially for the regions without higher surface heat flow, e.g., Qiangtang area in the northern Tibet (Wei et al., 2006; Shen et al., 1990).

  • A 40-km-thick continental crust in globally averaged sense (Mooney, 2007) can be divided into the upper, middle and lower layers together with a lowermost layer or crust-mantle transition zone (O'Reilly and Griffin, 2013). For non-cratonic areas, a 40-km-thick crust is assigned to consist of 10-km-thick upper crust, 6-km-thick middle crust and 24-km-thick lower crust (Fig. 1a). This crustal model with geothermal characteristics is constructed based on seismic, petrologic and geothermal data (Fig. 1, Table 1)(Furlong and Chapman, 2013; O'Reilly and Griffin, 2013; Jaupart and Mareschal, 2007).

    Figure 1.  (a) Example crustal model comprising of 4 layers: a 10-km-thick granitic upper crust (UC), a 6‑km‑thick middle crust (MC) of granitic rock and granulitic intrusions, a 16‑km‑thick granulitic lower crust (LC), and 8-km-thick lowermost crust or crust-mantle transition zone of granulitic rock and peridotitic intrusions. The crustal boundaries at 16 km and Moho at 40 km are fixed in all calculations, whereas the depths of other boundaries vary. In this sketch, granulitic and peridotitic intrusions are assumed to be one-third of the material in the middle crust and lowermost crust, respectively. (b) Corresponding profiles of heat flow (red), heat production (pink), and thermal conductivity (blue and purple). Blue line represents the thermal conductivity of a simple 2-layer crust composed of a 16‑km-thick granitic upper layer and a 24‑km-thick granulitic lower layer. Parameters correspond to the isotropic values listed in Table 1, suitably corrected for increasing pressure and temperature with depth (Furlong and Chapman, 2013). (c) Enlarged section of (b) from 8-18 km.

    Rock type Heat production Thermal conductivity
    (μW/m3) (W/m/K)
    Granitic mass 2 3.3
    Granulitic mass 0.45 2.6
    Granulitic intrusion (isotropic) 0.45 2.6
    Granulitic intrusion (anisotropic-vert/horiz) 0.45 1.56/2.6
    Peridotitic intrusion (isotropic) 0.02 2
    Peridotitic intrusion (anisotropic-vert/horiz) 0.02 1.2/2.0
    Volumes of granulitic and peridotitic intrusions are indicated in the figures and captions. For the anisotropic values (ANISO in the figures), the vertical thermal conductivities are taken to be 0.6 the horizontal thermal conductivities, equivalent to the weak anisotropy of typical gneissic rocks (Jaupart and Mareschal, 2007).

    Table 1.  Parameters used in the geothermal modeling (Furlong and Chapman, 2013; Jaupart and Mareschal, 2007)

    We use a 1D modeling method for steady-state heat conduction that accounts for temperature and pressure variations with depth (Furlong and Chapman, 2013). This approach is relatively simple to implement and can be adapted to handle laminated architectures. Following the 1D steady-state heat conduction equation, the temperature in a layer with constant heat generation Aand constant thermal conductivity k is

    with

    where (Tt, qt) and (Tb, qb) are the temperature and heat flow at the top and bottom of the layer, respectively, and z is the thickness of the layer. Once crustal lithologies and related heat productions and thermal conductivities are established, temperatures can be reliably extrapolated downwards with a thermal conductivity correction

    where T0 and TH are the temperature at the surface and depth H, respectively; and c and d are the pressure coefficient and temperature coefficient, respectively. The choice for the pressure and temperature coefficients in the following calculations is consistent with Furlong and Chapman (2013).

  • The surface heat flow is fixed at 60 mW/m2 for calculations in Figs. 2 and 3. For a crustal model in which granulitic intrusions are one-third of the volume of a generally granitic middle crust (10-16 km depth range) and the entire lower crust is granulitic, the temperature at the Moho is calculated to be~612℃ (MC 6 km in Fig. 2a), which is 10.2% higher than the predicted Moho temperature for a simple 2-layer granitic-granulitic crustal model (i.e., dT=10.2% in Fig. 2a). A similar high temperature is obtained for a model in which peridotitic intrusions are one-third of the volume of a generally granulitic lower crust (16-40 km depth range) and the upper-to-middle crust is entirely granitic (LC 24 km in Fig. 2b). For a crustal model that contains one-third of volumes of granulitic and peridotitic intrusions throughout the middle and lower crustal layers, respectively, the Moho temperature is calculated to be~676℃ (Fig. 2c) and dT=21.8%. Moreover, if the thermal conductivities of the granulitic and peridotitic intrusions are anisotropic (Table 1), then the Moho temperature could be as high as~753℃ with a dT value of 35.6% (Fig. 2d). Such a temperature in the presence of fluids could cause minor partial melting at high water fugacity.

    Figure 2.  Temperature versus depth for 60 mW/m2 surface heat flow for models in Fig. 1. (a) Isotropic (ISO) models with granulitic intrusions in MC with varying thicknesses and without peridotitic intrusions in LC. (b) Isotropic models without granulitic intrusions in MC and with peridotitic intrusions in LC with varying thicknesses. (c) Isotropic models with granulitic intrusions in MC and peridotitic intrusions in LC with varying thicknesses. (d) As for (c), but with anisotropic granulitic and peridotitic intrusions (ANISO; vertical thermal conductivities are assumed to be 0.6 the horizontal thermal conductivities; see Table 1). dT is the percentage of Moho temperature difference between the indicated models and the simple isotropic 2-layer crustal model.

    Figure 3.  A is a simple 2-layer isotropic model, whereas the other models contain anisotropic peridotitic components. B, C, and D contain a 6-km-thick homogeneous layer of anisotropic peridotitic rock at three different levels in the lower crust. E has an entire lower crust of isotropic granulitic rock with 25% anisotropic peridotitic intrusions (totally 6-km thick). F contains a lower crust of isotropic granulitic rock with intercalated layers of anisotropic peridotitic rock (totally 6-km thick) that progressively increases in thickness with depth. Diagram on the right shows profiles of temperature versus depth for the A-F models. Parameters are listed in Table 1, suitably corrected for increasing pressure and temperature with depth (Furlong and Chapman, 2013). There are two notable characteristics: (i) Moho temperatures for models C and E are almost the same with values approximately equal to the average Moho temperature of models B and D, and (ii) although models B-D contain the same volume of peridotitic rock, the Moho temperatures differ; F has the highest Moho temperature. These results demonstrate that the distribution of rock types and anisotropy have significant effects on Moho temperatures and that heat shielding effects can be substantial.

    It is interesting to note that computations yield the same~672℃ Moho temperature for a model with a single 6-km-thick layer of anisotropic peridotitic rock at 25-31 km depth (C in Fig. 3) as a model with the same volume of anisotropic peridotitic rock distributed uniformly as intrusions throughout a 24-km-thick lower crustal layer of granulites (E in Fig. 3). This temperature is very close to the average Moho temperature for models with single 6-km-thick layers of anisotropic peridotitic rock at 16-22 and 34-40 km (B and D in Fig. 3). This means the equivalences exist (i.e., C=E≈(B+D)/2 in Fig. 3). The minor difference in Moho temperature for the same volumes of granulitic and peridotitic rocks in the lower crust is caused by nonlinear temperature and pressure effects on thermal conductivity (Furlong and Chapman, 2013). Model F with laterally uniform anisotropic peridotitic intrusions that thicken with depth is an attempt to account for the expected increase in volume of ultramafic rock as the Moho is approached (O'Reilly and Griffin, 2013). The estimated Moho temperature for this model is~725℃.

    Because surface heat flow is markedly > 60 mW/m2 in many non-cratonic environments, the computational results presented here (Fig. 4) suggest that Moho temperature may exceed the solidus for crustal rocks in some regions in regardless of thermal conductivity anisotropy introduced by laminated structure and/or rock's intrinsic character. For example, when the surface heat flow is 80 mW/m2 the Moho temperature will be 1 100℃ for the model in Fig. 4, which would cause high degrees of partial melting in common crustal rocks (Thompson, 1999).

    Figure 4.  The model contains a lower crust of isotropic granulitic rock with intercalated layers of isotropic peridotitic intrusion (total of 3-km thick) that progressively increases in thickness with depth. The 24-km-thick lower crust is divided into a 10-km-thick granulitic layer, followed by a 8-km-thick intercalated layers of 12.5% isotropic peridotitic intrusion (total of 1-km thick), then a 4-km-thick intercalated layers of 25% isotropic peridotitic intrusion (total of 1-km thick), and a 2-km-thick intercalated layers of 50% isotropic peridotitic intrusion (total of 1-km thick). The right diagram shows profiles of temperature versus depth for different surface heat flows (40 to 90 mW/m2). Parameters used are listed in Table 1, suitably corrected for increasing pressure and temperature with depth (peridotitic intrusions). These results demonstrate that Moho temperature can exceed the solidus for crustal rocks in regions with surface heat flows larger than globally averaged value 70.9 mW/m2 (Furlong and Chapman, 2013) when taking into account of the distribution of rock types in regardless of anisotropic thermal conductivity.

  • Based on the results depicted in Figs. 2 and 3, it can be concluded that Moho temperatures are higher for (1) greater total thicknesses of the laminated structures, (2) greater thicknesses of granulitic rocks in the middle crust and peridotitic rocks in the lower crust, and (3) lower vertical thermal conductivities anywhere in the crust. These characteristics are natural heat shielding effects (Maldovan, 2013) because temperature-versus-depth relationships are dependent on fine-scale lithological variations regardless of the surface heat flow values (note that the same surface heat flow value was used for calculations in Figs. 2 and 3). Clearly, it is not possible to estimate reliable Moho temperatures on the basis of surface heat flow and average crustal composition alone, the distribution of lithologies and their physical properties are required (McKenzie et al., 2005).

  • The present study might overlap some previous researches though they were derived from different points of origin. For example, Furlong and Chapman (1987) found that depth distribution of crustal heat sources can be affected by the horizontal scale of crustal heterogeneity. This may cause overestimated the heat flux at the base of lithosphere in the cratons which is open to debate (Hasterok, 2013; Hasterok and Chapman, 2011; Jaupart and Mareschal, 2007). However, the mentioned study didn't elaborate on shielding effects and does not violate our results. Our results can be always true so long as basal heat flux keeps positive input from sub-lithosphere.

    Temperature-dependent thermal diffusivity has also been proposed as a mechanism for generating melting temperatures in the middle to lower crust (Gelman et al., 2013; Whittington et al., 2009), but its effect has not been related to fine-scale variations of crustal structure and therefore it is different from the model proposed in this study.

    To account for substantial lateral lithological heterogeneity, whatever for the present and previous studies, two-and three-dimensional thermal modeling codes need to be applied to temperature and rock property information provided by geophysical, geochemical and petrological data. The heat shielding effects that conceal these high Moho temperatures are strongly dependent on the distribution of the different lithologies.

  • All values of parameters in the calculation were rigorously chosen from published literatures (Furlong and Chapman, 2013; Jaupart and Mareschal, 2007). We mention that a well-fitting relation exists between electrical lithosphere-asthenosphere boundary (LAB) and surface heat flow (Eq. (3) in Artemieva, 2006). Combining this relation and 1D stead-state heat conduction equation, the average heat production A and conductivityk in the whole lithosphere can be estimated from the surface heat flow q0, sub-lithosphere contribution to heat flow qLAB as

    These relations are derived by assuming the temperatures are zero at surface and 1 300℃ at LAB, respectively. We can hence define a set of average A and kin terms of different combination values of heat flow at surface and LAB (Fig. 5). A reasonable range of heat flow at LAB may be in 5-22 mW/m2 (Hasterok, 2013). These confine the average heat production and conductivity of the lithosphere being 0.6-0.77 μW/m3 and 2.43-2.96 W/m/K (Fig. 5), respectively. For medians of 13.6 mW/m2 and 71.9 mW/m-2 of the heat flow at LAB and continental surface, the average lithospheric heat production and conductivity will be 0.7 μW/m3 and 2.7 W/m/K in continents (red diamond in Fig. 5), respectively, which are close to the statistical values of the lower crust from global petrological data (e.g., Furlong and Chapman, 2013). These estimations in turn give about 82 km for the average depth of LAB globally, which wonderfully coincides the results derived from seismic P-to-S conversion depth (Rychert and Shearer, 2009). The match strongly supports the values of parameters used in the calculations. Moreover, these values are convinced not extreme in the published measurements (ref. Appendix 4 in Jaupart and Mareschal, 2007) and also do not conflict with recent compilation of major Archean rocks (Merriman et al., 2013).

    Figure 5.  Cross-plot of heat production (red) and conductivity (deep blue) versus surface and LAB heat flows. The calculation is based on Eqss (4) and (5) in text. The purple cross indicates point for the averaging heat flow at surface (Furlong and Chapman, 2013) and at LAB (Hasterok, 2013).

    In addition, noting that, although the intrinsic anisotropy of thermal conductivity considered in the calculations of Fig. 3 might depart from the realistic rocks, which cannot be avoided due to paucity in the testing data, the seismic laminated structure in the lower crust (e.g., O'Reilly et al., 2010) can also be realized as macro-anisotropic in physics (Carcione et al., 1991) which results in the same thermal shielding effect that has been confirmed in material engineering (Narayana and Sato, 2012).

  • A well-known example of magmas present in the middle crust is from geophysical imaging in southern Tibet (Unsworth et al., 2005; Li et al., 2003; Wei et al., 2001; Makovsky and Klemperer, 1999; Nelson et al., 1996), which is not surprising since the surface heat flow is more than 90 mW/m2 there (Shen et al., 1990). However, super-wide band magnetotelluric data indicate that a lower resistivity ( < 4 Ω·m) zone also exists in the middle-to-lower crust of northern Tibet (Wei et al., 2006) where the surface heat flow is a negligible greater than the globally averaged level (Furlong and Chapman, 2013). In terms of results from previous studies showing coincidence of seismic bright spots (Makovsky and Klemperer, 1999) and low resistivity zone, show strong multiple reflectors on the top of and inside the low resistivity zone (Unsworth et al., 2005), and these strongly suggest that there is a typical heat shielding structure in the crust of northern Tibet. Supposing these strong multiple reflectors are layers of mafic (e.g., granulitic rock) and ultramafic (e.g., peridotitic rock) intrusions, the temperature at lower crust will easily cause the partial melting of granites at high water fugacity (Petford et al., 2000) if the volume of the intrusions is large enough.

    In summary, except for areas devoid of significant reflectors in the middle and lower crust, e.g., the Kaapvaal craton (Niu and James, 2002), heat shielding can affect practically any regions regardless of the surface heat flow values, level of heat input from the mantle, tectonic evolution and age. Heat shielding offers explanations as to why shear zonesand/or magmas are well developed in some middle crustal sections and not in others, and how significant lateral heat gradients can occur in the crust and subcontinental lithospheric mantle. This mechanism can also be extended to explain apparent delays in cooling of the mantle associated with plate subduction (van den Berg and Yuen, 2002).

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