PUBLICATIONS. Journal of Geophysical Research: Solid Earth

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1 PUBLICATIONS Journal of Geophysical Research: Solid Earth RESEARCH ARTICLE Key Points: The residual topography of the eastern NCC is about km higher than that of the western NCC A 2-D numerical model explains the observed dynamic topography, heat flux, and magmatism About 50% of destabilized NCC lithospheric materials remain in the shallow mantle and lithosphere of the NCC region Correspondence to: J. Huang, jshhuang@ustc.edu.cn Citation: Wang, Y., J. Huang, S. Zhong, and J. Chen (2016), Heat flux and topography constraints on thermochemical structure below North China Craton regions and implications for evolution of cratonic lithosphere, J. Geophys. Res. Solid Earth, 121, , doi: / 2015JB Received 21 SEP 2015 Accepted 3 APR 2016 Accepted article online 7 APR 2016 Published online 21 APR American Geophysical Union. All Rights Reserved. Heat flux and topography constraints on thermochemical structure below North China Craton regions and implications for evolution of cratonic lithosphere Yongming Wang 1,2, Jinshui Huang 1,2, Shijie Zhong 3, and Jiaming Chen 1,2 1 Laboratory of Seismology and Physics of Earth s Interior, School of Earth and Space Sciences, University of Science and Technology of China, Hefei, China, 2 Mengcheng National Geophysical Observatory, Hefei, China, 3 Department of Physics, University of Colorado Boulder, Boulder, Colorado, USA Abstract The eastern North China Craton (NCC) has undergone extensive reactivation during the Mesozoic and Cenozoic, while the western NCC has remained stable throughout its geological history. Geophysical and geochemical observations, including heat flux, surface topography, crustal and lithospheric thicknesses, and volcanism, show significant contrast between the eastern and western NCC. These observations provide constraints on thermochemical structure and reactivation process of the eastern NCC, thus helping understand the dynamic evolution of cratonic lithosphere. In this study, we determined the residual topography for the NCC region by removing crustal contribution to the topography. We found that the residual topography of the eastern NCC region is generally km higher than the western NCC. We computed a large number of two-dimension thermochemical convection models for gravitational instability of cratonic lithosphere and quantified surface heat flux and topography contrasts between stable and destabilized parts of cratonic lithosphere. These models consider different chemical buoyancy (i.e., buoyancy number B) and viscosity for the cratonic lithosphere. Our models suggest that to explain the difference in heat flux (25 30 mw/m 2 )and residual topography ( km) between the eastern and western NCC regions, the buoyancy number B is required to be ~ This range of B implies that as much as 50% of the original cratonic lithospheric material remains in the present-day eastern NCC lithosphere and its underlying shallow mantle and that the new lithosphere in the eastern NCC may be a mixture of the relics of old craton materials and the normal mantle. 1. Introduction Archean cratons are tectonically stable for billions of years and are characterized by low surface heat flux and thick mantle lithosphere that is seismically fast and chemically depleted [Carlson et al., 2005; Lee, 2006]. However, not all the cratons have been tectonically stable since their formation. The North China Craton (NCC), one of the oldest Archean cratons in the world, had undergone extensive modification and destruction during the Mesozoic and Cenozoic in its eastern part, while the western NCC has remained stable (Figure 1) [e.g., Menzies et al., 2007]. Geochemical and geophysical observations suggest that the mantle lithosphere of the eastern NCC in the Ordovician was cold, thick (~200 km), and refractory and had an Archean age, but it is thin (~80 km), hot, and relatively fertile at present [Griffin et al., 1998; Menzies et al., 2007; Xu, 2001; Zhu et al., 2012a]. By contrast, the lithospheric thickness of the western NCC is ~200 km [Chen et al., 2009; Zhu et al., 2012a]. The reactivation of the eastern NCC may have been initiated in the Jurassic around Ma and may have lasted for ~100 Myr until the late Cretaceous, as indicated by the large-scale deformation, magmatic activities, and basin formation during these time periods. However, the western NCC especially the central Ordos Basin has little magmatism [Xu et al., 2009; Zhu et al., 2012b]. Present-day surface heat flows are ~65 mw/m 2 and 40 mw/m 2, in the eastern and western NCC regions, respectively [Hu et al., 2000], but it is suggested that the heat flow in the eastern NCC has been as low as ~40 mw/m 2 in the Paleozoic [Griffin etal.,1998;xu, 2001] and peaked to ~80 mw/m 2 in Mesozoic and Cenozoic [e.g., Menzies et al.,2007].significant variations in surface elevation and crustal thickness also exist between the eastern and western NCC. The eastern NCC s elevation is at ~200 m, while the western NCC is significantly (1 2 km) higher (Figure 1). Seismic studies show that the crustal thickness of the eastern NCC is ~30 km, while it is ~45 km in the west [Bao et al., 2013;Cheng et al., 2013; Li et al., 2014]. Such topography and thickness variations of crust and lithosphere are responsible for the gravity anomalies between the eastern and western NCC [e.g., Chen, 2010]. WANG ET AL. HEAT FLUX AND TOPOGRAPHY CONSTRAINTS 3081

2 These observations of the eastern NCC reactivation and the contrast between the eastern and western NCC provide a unique opportunity to study the stability and evolution of cratonic lithosphere. The stability of cratonic lithosphere is mainly controlled by lithospheric viscosity [e.g., Lenardic et al., 2003; O Neill et al., 2008]. It has been proposed that the reactivation of the eastern NCC is largely caused by water-induced lithospheric viscosity reduction, while such effects on the western NCC may be small [e.g., Zhu et al., 2012a]. Several mechanisms have been proposed for the reactivation of the eastern NCC, and they include subduction induced thermochemical convective erosion [Griffin et al., 1998; Xu, 2001;Zheng et al., 2006], lithospheric delamination [Gao et al., 2004; Wu et al., 2005], peridotite-melt interaction [Zhang et al., 2005; Zheng et al., 2007], and episodic gravitational instabilities [Wang et al., 2015]. Figure 1. (a) Crustal thickness, (b) surface topography, and (c) residual topography for the NCC and its adjacent area. Orange lines sketch the location of the NCC. Black dashed line outlines the Ordos Basin. White lines represent geological features as indicated: NSGL, North south Gravity Anomaly Line; QL-DB, Qinling-Dabie Orogenic Belt; BB, Bohai Bay; and TFZ, Tanlu Fault zones. An important question that remains unclear is whether the entire lithospheric mantle of the eastern NCC has been removed and replaced with underlying normal mantle material during the reactivation or if there remains relicts of the Archean lithospheric mantle in the present lithosphere [Gao et al., 2002; Menzies and Xu, 1998; Wu et al., 2005; Zheng et al., 2001]. The existence of eclogitic lower crust component in Jurassic volcanic rocks has been suggested as evidence for removal of the lower crust and for complete removal of Archean lithospheric mantle [Gao et al., 2008, 2004]. This is also supported by Re-Os isotopic studies on Cenozoic basalts, which indicate that the mantle lithosphere beneath the eastern NCC is young and of oceanic type [Gao et al., 2002; Wu et al., 2006]. However, other studies show that in the Cenozoic basalts in the eastern NCC (e.g., in Kuandian, Yangyuan, and Fansi), the Re-Os model ages could be Archean- Paleoproterozoic [e.g., Wu et al., 2006; Xu et al., 2008]. The presence of both high Mg and low Mg number peridotite xenoliths in the Cenozoic basalts in the WANG ET AL. HEAT FLUX AND TOPOGRAPHY CONSTRAINTS 3082

3 eastern NCC was also proposed to support the co-existence of the residual ancient refractory mantle and oceanic mantle [Wu et al., 2008; Zheng et al., 2007, 2001]. As an alternative model to the subduction model for reactivation of cratonic lithosphere [Lenardic et al., 2003; O Neill et al., 2008, 2010], Wang et al. [2015] suggested that a gravitational instability model [e.g., Jaupart et al., 2007] may explain some of the main observations associated with the eastern NCC reactivation, including the episodic and long-lasting magmatic activities and the formation and foundering of the lower eclogitic crust. An important feature of the instability model by Wang et al. [2015] is that some of the destabilized cratonic lithospheric mantle, due to its compositional buoyancy, comes back to be part of the newly formed lithosphere, as first observed in laboratory studies [Jaupart et al., 2007; Fourel et al., 2013]. Consequently, in this model, the present-day lithosphere after the reactivation may contain a significant amount of original, compositionally buoyant cratonic lithospheric materials. This result supports the geochemical evidence of existing remnants of cratonic lithosphere after the NCC reactivation. Given that the thermal and compositional structures of a cratonic lithosphere play a controlling role in the surface expressions, such as topography and heat flux [Elkins-Tanton, 2005], we hypothesize that surface topography and heat flux in the eastern and western NCC regions may provide constraints on the amount of cratonic mantle materials present in the present-day lithosphere, thus constraining the mechanism of reactivation. The study in Wang et al. [2015] was focused only on the stability conditions for cratonic lithosphere. In this paper, using the differences of residual topography and heat flux between the eastern and western NCC, we seek to constrain the amount of the cratonic mantle in the reactivated eastern NCC lithosphere. We formulate numerical models of mantle convection and lithospheric instability that include both the unstable eastern NCC and stable western NCC regions. We will first determine the residual topography difference between the eastern and western NCC regions, by removing the isostatic topography of the crust from the observed surface topography. We will then describe the model setup and present the numerical results. Before presenting conclusions, we will discuss the implications of our results for the evolution of the NCC and the dynamics of cratonic lithosphere in general. 2. Residual Topography of the NCC Surface topography in continental regions is mainly caused by variations in crustal thickness. The residual topography is the topography difference between the observed topography and the calculated isostatic topography due to crustal thickness variations [e.g., Panasyuk and Hager, 2000]. Because the residual topography may be largrly related to the mantle dynamics, it is also called dynamic topography. According to the Airy isostatic model, the isostatic topography, h iso, relates to the crustal thickness, H, as h iso ¼ ρ m ρ c ðh H 0 Þ (1) ρ m where ρ m and ρ c are the densities of the mantle and crust, respectively, and H 0 is a compensation depth. A number of studies have determined the crustal thickness variations in China using different seismic methods [e.g., Bao et al., 2013; Ge et al., 2011; Li et al., 2006, 2014; Wei et al., 2011]. Here we adopt the crustal thickness model from Li et al. [2014], which is a compiled data set of crustal thickness from receiver function analyses. The crustal model is for the whole Chinese mainland with spatially varying resolution, but it has a relatively high resolution in the NCC region [Li et al., 2014] (Figure 1a; note that some areas of the NCC are not included due to the lack of data). The crustal thickness is km in the stable Precambrian Ordos Basin in the western part of the NCC, but is ~30 km in most part of the eastern NCC, such as the North China Basin (Figure 1a). The transition from the thick to thin crust is roughly along the North south Gravity Anomaly Line. The surface topographic data are derived from the global high resolution Digital Topographic Model (DTM2006.0) [Pavlis et al., 2007] (Figure 1b). The topography is relatively high at km in the western NCC region but is only hundreds of meters in the eastern part (Figure 1b). The topography shows a positive correlation with the crustal thickness, suggesting that the topography is mostly produced by the crustal isostasy. In calculating the isostatic topography h iso, parameter values used in equation (1) are: ρ c = 2.8 g/cm 3, ρ m = 3.3 g/cm 3, and H 0 = 35 km, which are consistent with that used in CRUST1.0 model [Laske et al., 2013] and other studies [Ge et al., 2011; Wei et al., 2011]. The isostatic topography is not very sensitive to ρ c, ρ m, WANG ET AL. HEAT FLUX AND TOPOGRAPHY CONSTRAINTS 3083

4 Figure 2. Model schematics show (a) model setup and boundary conditions, (b) initial temperature, and (c) initial effective viscosity profiles. The thick dashed line in Figure 2c is for the viscosity of the stable, left side of the cratonic lithosphere, which is 10 times higher than that of the right side. and H 0. Since we are mostly concerned about the residual topography difference between the eastern and western NCC regions, we consider these parameters as fixed in this study. The residual topography of the NCC area after removing the crustal isostatic topography is shown in Figure 1c. The residual topography varies generally from about 2 km in the western part of the NCC to about 2 km in the eastern part. The largest negative residual topography occurs in the westernmost part of the NCC, where the lithosphere and crust may be influenced by the uplift of the Tibetan Plateau [Zhao et al., 2013]. Therefore, we do not include this area in the subsequent discussion. The residual topography in the stable central part of the Ordos Basin ranges from 0 to 0.5 km (Figure 1c). The residual topography in the eastern part of the NCC is mostly between 0.5 and 1.5 km. The area with negative residual topography in the eastern NCC is located in the Bohai Bay area, and the crust in this area is the thinnest (Figures 1a and 1c). The averaged difference in residual topography between the eastern and the western NCC regions is about km, with the eastern NCC region higher. 3. Numerical Model Setup The model setup is similar to that of Wang et al. [2015]. The model includes two compositionally distinct layers (Figure 2). The top layer is 200 km thick and chemically buoyant, representing the cratonic lithospheric mantle. The bottom layer is for the normal convective mantle (Figure 2a). The nondimensional governing equations are u ¼ 0 (2) P þ η u þ T u þ RaðT BCÞez ¼ 0 (3) T t þ u T ¼ 2 T (4) C þ u C ¼ 0 (5) t where u, P, η, T, and C are the velocity, pressure, viscosity, temperature, and composition, respectively, and e z is the unit vector in vertical direction. The composition C is set to be 1 for cratonic lithosphere and 0 for other mantle materials. Ra and B are a Rayleigh number and compositional buoyancy number that are defined as Ra ¼ αρ 0gΔTD 3 κη 0 (6) B ¼ Δρ ρ 0 αδt (7) where α is the coefficient of thermal expansion, ρ 0 is the reference density, g is the gravitational acceleration, D is the thickness of the box, κ is the coefficient of thermal diffusivity, η 0 is the reference mantle viscosity, ΔT is the temperature difference across the box, and Δρ is the intrinsic compositional density difference between the normal mantle and cratonic lithosphere. The scales for length, time, and temperature are D, D 2 /κ, andδt, respectively. WANG ET AL. HEAT FLUX AND TOPOGRAPHY CONSTRAINTS 3084

5 The viscosity employed in this study is compositional-, temperature-, depth- and strain rate-dependent, and the effective composite viscosity is defined as [e.g., Wang et al., 2015] η ¼ η TC 1 þ η TC ε τ T n 1 n (8) where ε is the second invariant of the strain rate tensor and τ T and n are the transition stress and the stress exponent, respectively [Hirth and Kohlstedt, 2003], η TC represents the depth-, composition- and temperaturedependent viscosity that is expressed as η TC ¼ η h η c e E ð1 TÞ (9) where η c and η h reflect the composition- and depth-dependence, respectively, and E * =E/(RΔT) is the dimensionless activation energy with R as the gas constant and E as the activation energy. Although it has been suggested that the viscosity contrast between the cratonic lithosphere and the asthenosphere may not exceed a factor of 100 [e.g., O Neill et al., 2008], with the consideration of stress-dependent viscosity, we set η c to be 1000 for cratonic lithosphere and 1 for the normal mantle, respectively, following Wang et al. [2015]. The depth-dependence parameter, η h, is set to be 1 for upper mantle (i.e., above a depth of 410 km), 5 for the transition zone (i.e., between depths of 410 km and 660 km), and 30 for lower mantle (i.e., below a depth of 660 km) (Figure 2c). A cutoff of a factor of 10 3 in nondimensional viscosity is employed for η TC in order to limit the viscosity variation to make the numerical simulation more efficient. As shown in Wang et al. [2015], a large E would cause the lithosphere to be stable, and a relatively small E = 120 kj/mol is used here. The model is in a two-dimension box with an aspect ratio of 2. As seen in Wang et al. [2015], once the instabilities initiate, they will propagate through the whole cratonic lithosphere episodically to destabilize the entire lithosphere. The effective composite viscosity (equation (8)) for the left half of the cratonic lithosphere is set to be 10 times higher than that of the right half, and the left and right sides of the model lithosphere are used to simulate the stable western and unstable eastern NCC, respectively (Figure 2c). Previous studies have shown that the stability of the buoyant cratonic lithosphere is controlled by the lithospheric viscosity (or Rayleigh number) [Jaupart et al., 2007] and for non-newtonian viscosity by the lithospheric viscosity just before the onset of instability [Wang et al., 2015]. Therefore, similar to Wang et al. [2015], a local Rayleigh number associated with the cratonic lithosphere is computed for each case: Ra l ¼ αρ 0gΔTδ 3 (10) κη l where δ and η l are the thickness and the averaged viscosity of the cratonic lithosphere, respectively. The averaged viscosity η l is determined from the lithospheric viscosity weighted by strain rate just before the onset of instability in the cratonic lithosphere, and the onset time is defined as the time when the timedependent averaged flow velocity of the cratonic lithosphere first surpasses 1% of its maximum [Wang et al., 2015]. For reference, the normal mantle viscosity, η m, is also calculated at the same time and with the same method as those for calculating η l. Because the left half of the lithosphere is set to be stable, the calculation for Ra l is only performed for the right half. In our model, the top boundary is fixed, while the bottom and sidewall boundaries are free-slip (Figure 2a). The temperatures at the surface and the bottom boundaries are fixed at 0 and 1, respectively, and the side boundaries are thermally insulating (Figure 2a). For the initial conditions, the temperature is set to increase linearly with the depth from 0 at the surface to be 1 at the bottom of the cratonic lithosphere and a uniform temperature of 1 is for the underlying normal mantle (Figure 2b). A random temperature perturbation with a magnitude of 0.01 is superimposed on the whole model. The governing equations (2) (5) are solved with finite element code Citcom, in which the composition field is solved with a tracer method [McNamara and Zhong, 2004; Moresi et al., 1996; Tackley and King, 2003]. The model box is divided into elements, and initially, each element contains 16 tracers to represent the compositionally distinct cratonic lithosphere and the regular mantle. The model parameter values are listed in Table 1. In our models, dynamic topography is determined from the normal stress acting on the surface σ zz and the dimensional values of the topography is computed with w=αδtσ zz D/Ra. We also compute mantle isostatic topography that is entirely due to temperature and/or compositional variations (i.e., the thermal and WANG ET AL. HEAT FLUX AND TOPOGRAPHY CONSTRAINTS 3085

6 Table 1. Model Parameters and Values Box Thickness (D) 1000 km Lithospheric thickness (δ) 200 km Thermal expansivity (α) /K Reference density (ρ 0 ) 3300 kg/m 3 Gravitational acceleration (g) 9.8 m/s 2 Surface temperature (T s ) 873 K Reference temperature (ΔT ) 750 K Thermal diffusivity (κ) 10 6 m 2 /s Transition stress (τ T ) 0.5 MPa Stress exponent (n) 3.5 Activation energy (E ) 120 kj/mol Gas constant (R) 8.3 J/(mol K) chemical buoyancy) [e.g., Huang and Zhong, 2005; Jarvis and Peltier, 1982]. The mantle isostatic topography differs from the dynamic topography, because it does not consider the full dynamics (e.g., no pressure effect). However, due to its simplicity, the mantle isostatic topography provides a useful insight into the dynamic topography [Huang and Zhong, 2005]. Vertical integrations of temperature and composition, i.e., F T ¼ 1 1 d½ Tx; ð zþ T mšdz and F C ¼ 1 1 dbcðx; zþdz; (11) represent the horizontal buoyancy variations caused by the temperature and composition, respectively. In equation (11), T m is the mantle temperature and d is the nondimensional thickness of the layer, in which the thermal and chemical buoyancy are considered. The averages of these buoyancies over a horizontal span of x 1 to x 2 are F TA ¼ 1 x 2 x 1 x2 x d½ Tx; ð zþ T mšdz dx and F CA ¼ 1 x 2 x 1 x2 x d BC x; z dx: (12) The thermal and chemical buoyancy may be converted to mantle isostatic topography, w TC, by assuming isostatic compensation [e.g., Jarvis and Peltier, 1982; Davaille and Jaupart, 1994]: w TC ¼ DαΔT 1 1 d½ Tx; ð zþ T mšdz þ 1 1 d BC ð x; z Þdz : (13) 4. Numerical Results Lithospheric instability develops when the local Rayleigh number of the lithosphere Ra l is larger than some critical value, depending on buoyancy number B [e.g., Jaupart et al., 2007; Wang et al., 2015]. We have computed a total of 33 cases with different lithospheric Rayleigh number Ra l and buoyancy number B (Table 2). For the cases with small Ra l (i.e., marked as stable in Table 2), the models are computed for at least 4.5 Gyr. For the cases in which the instabilities developed for the right part of the cratonic lithosphere, the models are run for long enough to include at least 300 Myr after the onset of instabilities. For all cases, the left part of the cratonic lithosphere is always stable A Reference Case We first present a case with B = 0.4 and Ra l = 2930 (case B43 in Table 2) as a reference case. The gravitational instability process for the cratonic lithosphere in our models here is similar to that in Wang et al. [2015]. Figure 3 shows several snapshots of temperature and composition, as well as surface topography and heat flux for this case. Before the instabilities develop on the right half of the cratonic lithosphere, the underlying mantle is already in vigorous convection because of its small viscosity. This sublithospheric convection induces small perturbations to the cratonic lithosphere and the mantle, but they do not produce significant topography and heat flux anomalies at the surface owing to the small amplitude of these perturbations. The instabilities in the cratonic lithosphere lead to increased surface topography and heat flux, although the heat flux anomalies appear a little later than that of topography because it takes time for thermal anomalies to diffuse through the lithosphere to the surface (Figures 3b and 3c). For this case, it takes about 53 Myr to reactivate the entire right half of the lithosphere, which is similar to the time scales reported by Wang et al. [2015]. Because the instabilities develop at shallow depth of the lithosphere, the thermal boundary layer thins significantly (Figure 3c). The detachment of the first cratonic lithosphere blob causes a large increase in surface topography and heat flux (Figure 3c). As the mantle cools, the thermal boundary layer in the reactivated region thickens with time, causing the topography and heat flux to decrease gradually (Figure 3d). WANG ET AL. HEAT FLUX AND TOPOGRAPHY CONSTRAINTS 3086

7 Table 2. Some Input and Calculated Parameters Case No. B Ra Ra l a η l a (10 21 Pa s) ηm a (10 21 Pa s) B e B e B e B04 b 0 1.0e B e B e B e B14 b e B e B e B e B24 b e B e B e B e B e B35 b e B e B e B e B e B e B46 b e B e B e B e B e B55 b e B e B e B e B e B65 b e a Ral, η l, and η m are calculated at the onset of lithospheric instabilities in the right half of the lithosphere if the instabilities develop there; otherwise, they are the averages for the last 100 Myr of each model. b These cases are considered stable. Since the reactivation reaches the shallow part of the cratonic lithosphere, the old thermochemical boundary layer has almost been entirely destroyed and removed (Figures 3c and 3d). However, some of the destabilized cratonic lithospheric mantle materials would return back to the lithosphere due to their compositional buoyancy (Figure 3e). After the reactivation of the right half of the cratonic lithosphere is completed, a new thermochemical boundary layer, or a new lithosphere with a mixture of cratonic lithosphere and normal mantle materials, has been developed (Figures 3d 3f). At this stage, the new thermochemical boundary layer is in a dynamic quasi-steady state. The new boundary layer thickens as the system cools, and it becomes unstable again at a certain stage (Figures 3e and 3f). This process could develop repeatedly and last for a long time. The surface topography and heat flux vary accordingly with the change of the thermochemical boundary layer (Figure 3). During the reactivation process, the surface topography and heat flux of the stable left half of the lithosphere have little variation (Figure 3). In order to compare the reactivated right half with the stable left half of the lithosphere, we calculate the averaged dynamic topography (i.e., due to σ zz ) and heat flux for the right and left parts at different times. In computing these averages, the results within ~50 km distance from the joint of the left and right parts (i. e., in the transitional region from the unstable to stable parts) are excluded to avoid potential bias caused by the abrupt viscosity jump there. Figure 4a shows the difference of the averaged topography between the right and left parts (i.e., referred to as averaged topography contrast hereafter), and Figure 4b shows the average heat fluxes for the right and left parts, respectively. As a comparison, the maximum of the differences of the topography between the right and left parts (i.e., maximum topography contrast) and the maximum of the heat flux on the right part are also included in Figures 4a and 4b, respectively. For this reference case, before the onset of instabilities at ~360 Ma, the topography contrast stays at zero, and the surface heat fluxes on both the left and right sides are at ~10 mw/m 2 (Figures 4a and 4b). The slight decrease in heat flux with time results from the cooling of the lithosphere. Note that because our model does not include the crust, the heat flux in this study is the mantle heat flux, and ~10 mw/m 2 mantle heat flux is rather typical for cratonic regions [Jaupart and Mareschal, 2011, 2012]. The pulses in topography contrast and heat flux at different times correspond to instability events in the unstable, right part of the lithosphere (Figures 4a and 4b). While the heat flux on the right side is in a quasi-steady state, the topography contrast shows a decreasing trend. This may be caused partly by the effect of faster secular cooling on the right side of the box after the reactivation (Figures 3e, 3f, and 4b) and partly due to the mixing of the buoyant cratonic lithospheric mantle materials with the normal mantle (Figures 3e and 3f). WANG ET AL. HEAT FLUX AND TOPOGRAPHY CONSTRAINTS 3087

8 Figure 3. Six snapshots of temperature, composition, surface heat flux Q, and surface dynamic topography w for the reference case (case B43, and B =0.4,andRa l = 2930). Times for different snapshots are shown for each group. The colors for composition are used only to indicate its initial position. In order to understand the variations in the topography contrast, we computed the averaged chemical and thermal buoyancy for the left and right sides of the model at different times using equation (12) (Figures 4c and 4d). Two different depths are considered for the integrals: one for the top 200 km and the other for the whole depth. Because the left half of the cratonic lithosphere is stable, the chemical buoyancy for the left half of the lithosphere (i.e., the top 200 km) stays unchanged with time. However, the chemical buoyancy for the WANG ET AL. HEAT FLUX AND TOPOGRAPHY CONSTRAINTS 3088

9 Figure 4. Time dependence of (a) topography contrast Δw,(b)heatflux Q, (c) chemical buoyancy F CA, and (d) thermal buoyancy F TA for case B43. In Figure 4a, the blue and red lines represent the averaged and maximum topography contrast between the right and left halves of the lithosphere, respectively. The blue and red dashed lines represent mantle isostatic topography contrast from thermochemical buoyancy over the top 200 km thick layer and the whole model depth, respectively. In Figure 4b, the blue and red lines represent the averaged and the maximum heat flux for the right half of the lithosphere, respectively, and the green line is the averaged heat flux for the left half. In Figures 4c and 4d, the solid and dashed lines represent the averaged buoyancy for the right and the left halves, respectively. The blue and red colors represent buoyancy over the top 200 km thick layer and the whole model depth, respectively. right half decreases significantly after the onset of instability (Figure 4c). Similar features can be seen for thermal buoyancy for the top 200 km (i.e., the lithosphere) except that the thermal buoyancy for the right half of the lithosphere increases after the instability (Figure 4d). Thermal buoyancy integrated for the whole mantle depth shows similar time-dependence to that for the top 200 km but with smaller amplitude of variations (Figure 4d). The destabilized, cold lithospheric mantle sinks into the deep mantle and cools the mantle there [e.g., Huang et al., 2003]. While this vertical mixing process causes significant increase in lithospheric temperature, it has a less effect on overall mantle temperature. The chemical buoyancy of the right half of the box for the whole depth decreases with time, while the chemical buoyancy of the left half of the box for the whole depth increases with time after the instabilities developed (Figure 4c). The increase in the left half of the box is equal to the reduction in the right half (Figure 4c). This is because the instabilities bring some buoyant cratonic lithospheric mantle materials from the right half of the box to the left half (Figures 3c 3f). The thermal and compositional buoyancy is converted to mantle isostatic topography, using equation (13). The contrast in mantle isostatic topography between the left and right sides is then computed for different times (Figures 4a). Both of mantle isostatic topography contrasts for the top 200 km and the entire mantle depth have a similar variation trend to dynamic topography (Figure 4a). However, the mantle isostatic topography contrast for the top 200 km of the model (i.e., the lithosphere) shows a better agreement with the dynamic topography contrast for the later stage when the convective mantle is more homogenized (Figures 3e and 3f), but at the early stage of instabilities, when significant structures exist in the mantle (Figures 3c and 3d), the isostatic topography for the whole box agrees better with the dynamic topography (Figure 4a). This suggests that most of the surface topography variations could be attributed to the change in temperature and composition in the lithosphere when its underlying mantle is largely homogenized (Figure 4a). For this reference case (case B43), the time-averaged topography contrast for 200 Myr after the onset of lithospheric instabilities is ~560 m with the reactivated side at higher elevation, while the time-averaged maximum topography contrast is ~950 m. In this study, 200 Myr is chosen for computing time average because the onset of the eastern NCC occurred ~200 Myr ago. Notice that the topography contrast generally decreases with time for the last 50 Myr of this 200 Myr duration (Figure 4a). At 200 Myr following the onset, the averaged topography contrast is ~560 m, similar to the time-averaged. The maximum heat flux in the destabilized part could reach ~90 mw/m 2, but the averaged heat flux for the destabilized part is ~40 mw/m 2 at ~150 Myr after the onset of instability (Figure 4b). Similar to the topography contrast, heat flux for the right WANG ET AL. HEAT FLUX AND TOPOGRAPHY CONSTRAINTS 3089

10 Figure 5. Snapshots of temperature, composition, surface heat flux, Q, and topography, w. for case B12 (B =0.1andRa l = 11800). side also generally starts to decrease ~150 Myr following the onset of instabilities. The time-averaged heat flux over the 200 Myr following the onset for the right part is ~24 mw/m 2, while the heat flux on the stable, left side is ~8 mw/m 2 with no significant change Cases With Different Buoyancy Number B The dynamics of cratonic lithospheric instability depends critically on buoyancy number B [Wang et al., 2015; Jaupart et al., 2007]. In order to better understand the variations in the topography and heat flux, we calculate WANG ET AL. HEAT FLUX AND TOPOGRAPHY CONSTRAINTS 3090

11 Figure 6. Time dependence of the (a) topography contrast Δw, (b) heat flux Q, (c) chemical buoyancy F CA, and (d) thermal buoyancy F TA for case B12. Line descriptions are the same as that in Figure 4. a large number of models with varying B (Table 2). Results for a case with a smaller buoyancy number (case B12 with B = 0.1 and Ra l = in Table 2) than our reference case are shown in Figures 5 and 6. While the general results of case B12 are similar to those of the reference case, several aspects deserve to be highlighted, due to the influence of a smaller buoyancy number. (1) With a smaller B, it takes a much shorter time (i.e., several megayears) to reactivate the entire right half of the cratonic lithosphere (Figure 5), consistent with Wang et al. [2015]. (2) More cratonic lithosphere is destabilized and removed, and this gives rise to larger difference in thermal buoyancy between the right and left parts (Figure 6d). (3) More chemically buoyant cratonic lithosphere is removed, although the difference in chemical buoyancy between the right and left parts is smaller because of the smaller B (Figure 6c). (4) The topography contrast is much larger because of the larger difference in thermal buoyancy and smaller difference in chemical buoyancy between the stable and unstable parts (Figure 6a). (5) For the destablized right part, the heat flux is much larger than that for a larger B (Figure 6b). For cases with very small buoyancy numbers (e.g., B 0.1), the cratonic lithosphere is easier to be removed and the mantle cools faster. Therefore, these cases have a relatively large viscosity, and hence a relatively thick thermal boundary layer and low surface heat flux (Figures 5e and 5f). For case B12, the time-averaged topography contrast and heat flux for the 200 Myr time span following the onset of instability are ~2040 m and ~26 mw/m 2, respectively (Figures 6a and 6b). The averaged topography contrast and heat flux on the right side at ~200 Myr following the onset are ~1770 m and ~23 mw/m 2, respectively (Figures 6a and 6b). Even though this case (case B12) has a smaller buoyancy number than the reference case, because of the influences of low temperature and high viscosity as pointed out above, its heat flux is compatible with that of the reference case. The results for a case with a larger buoyancy number (case B62 with B = 0.6 and Ra = 1460; Table 2) than that for the reference case are shown in Figures 7 and 8. Compared with the reference case, a larger B leads to a longer time (~100 Myr for case B62; Figure 7) to destabilize the entire right side of the lithosphere, and it also causes less thermal and chemical perturbations to the lithosphere, leading to the thicker destabilized thermal boundary layer (Figure 7). Consequently, there are smaller variations in the thermal and chemical buoyancy, smaller heat flux (Figures 8b 8d), and smaller topography contrast between the stable and unstable parts of lithosphere (Figure 8a). The time-averaged topography contrast and heat flux in the reactivated region over 200 Myr following the onset are ~180 m and ~13 mw/m 2, respectively. The averaged topography contrast and heat flux are ~80 m and ~12 mw/m 2, respectively, at ~200 Myr after the onset (Figure 8a). Figures 9a and 9b show the averaged topography contrast and heat flux contrast between the destabilized right and stable left parts of the lithosphere at ~200 Myr after the onset for cases with different buoyancy number B and lithospheric viscosity (i.e., Rayleigh number Ra l ) listed in Table 2. For comparison, the time-averaged WANG ET AL. HEAT FLUX AND TOPOGRAPHY CONSTRAINTS 3091

12 Figure 7. Snapshots of temperature, composition, surface heat flux, Q, and topography, w. for case B62 (B = 0.6 and Ra l = 1460). topography contrast and heat flux contrast over 200 Myr after the onset are shown in Figures 9c and 9d. The averaged lithospheric viscosities at or over 200 Myr are also shown as different colors in Figure 9. It appears that cases with larger B also have larger lithospheric viscosities, especially for the time-averaged results (Figures 9c and 9d). This is because the lithosphere in many cases that we compute is close to marginally stable, and the critical Rayleigh number for this two-layer system generally increases with B [Jaupart et al., 2007; Wang et al., 2015]. However, we do not find an apparent dependence of topography and heat flux contrasts on lithospheric viscosities for a given B (Figure 9), especially for those at ~200 Myr (Figures 9a and 9b). WANG ET AL. HEAT FLUX AND TOPOGRAPHY CONSTRAINTS 3092

13 Figure 8. Time dependence of the (a) topography contrast Δw, (b) heat flux Q, (c) chemical buoyancy F CA, and (d) thermal buoyancy F TA for case B62. Line descriptions are the same as that in Figure 4. The topography contrasts between the stable and destabilized regions of the lithosphere at ~200 Myr or averaged over 200 Myr following the onset decrease with increasing B (Figures 9a and 9c). For cases with a smaller B, the instabilities thin the thermal boundary layer more, leading to more thermal buoyancy for the destabilized part of the lithosphere (Figures 5 and 6d) and to a larger influence of thermal buoyancy on the topography contrast. The topography contrasts are km and km at ~200 Myr, for B = 0.1 and 0.6, Figure 9. Topography contrast Δw (a and c) and heat flux contrast ΔQ (b and d) between the (right column) unstable and (left column) stable parts of the lithosphere versus buoyancy number B. Figures 9a and 9b show data at ~200 Myr after the onset of lithospheric instability, and Figures 9c and 9d are for the time-averaged results over the 200 Myr following the onset. The shaded zones in Figures 9a and 9b represent the range of observed residual topography and heat flux contrasts, respectively. The colors in Figures 9a 9d represent the averaged viscosity of the destabilized (right part) lithosphere either at ~200 Myr (Figures 9a and 9b) or for time-averaged over 200 Myrs after the onset (Figures 9c and 9d). WANG ET AL. HEAT FLUX AND TOPOGRAPHY CONSTRAINTS 3093

14 Figure 10. (a) Averaged composition in the top 200 km of the mantle on the destabilized right side, C L, at 200 Myr after the onset versus buoyancy number B. The colors in Figure 10a represent the averaged viscosity of the destabilized (right part) lithosphere at ~200 Myr after the onset. (b) Horizontal averaged composition (thin lines) and temperature (thick lines) of case B43 for the right part (solid lines) and the left part (dashed lines) at ~200 Myr after the onset. respectively (Figures 6a, 8a, and 9a). Heat flux contrasts also show a clearly decreasing trend for increasing B, except for the cases with B 0.1 (Figures 9b and 9d). The heat flux contrast at ~200 Myr following the onset reaches ~35 mw/m 2 for B~0.4 (Figure 9b), although the time-averaged heat flux contrast is smaller (Figure 9d). For large B, the decreasing trend of heat flux with increasing B results from small instability-induced perturbations of the lithospheric thermal structure (Figures 9b and 9d). We have also quantified the averaged composition in the top 200 km of the model for the destabilized region at ~200 Myr following the onset of lithospheric instability for all the cases (Figure 10). As discussed earlier, when buoyancy number B is relatively small, the buoyant cratonic lithospheric materials can be readily removed and mixed with the underlying mantle. However, for large B, the cratonic lithospheric materials are not as easy to be removed, and even if they are removed, they have a great tendency to return to the shallow depths, due to their large compositional buoyancy. Due to the limitation of 2-D models in removing materials out of the box, the destabilized materials, after losing their negative buoyancy, tend to move upwards locally. Figure 10 shows that the averaged composition for the top 200 km increases with increasing B. ForB~0.4, the averaged composition is between 0.25 and 0.55, implying that ~25 55% of original cratonic lithospheric material remains in the top 200 km at ~200 Myr following the onset. For B~0.5, this percentage increases to ~60 70% (Figure 10a). Similar to the topography and heat flux, the averaged composition does not appear to depend on lithospheric viscosity for a given B (Figure 10a). 5. Discussions 5.1. Heat Flux Anomalies, Formation of Eclogite, and Buoyancy Number B The presence of mixture of eclogite and cratonic lithospheric mantle components in the Jurassic volcanic rocks [e.g., Gao et al., 2004, 2008] suggests that in the early stage of NCC reactivation there is significant amount of heat flux supplied to the lower crust [e.g., Jull and Kelemen, 2001]. Our numerical models show that in the early stage of the reactivation process, the instability-induced heat flux can increase significantly (Figure 4b), which could increase the temperature in the lower crust to help eclogite formation. During the early reactivation, the maximum heat flux could peak at ~60 mw/m 2 locally, but averaged over the region, the heat flux can reach ~30 mw/m 2 in our numerical model (e.g., Figure 4b). Therefore, a surface heat flux of ~100 mw/m 2 is highly possible if crustal radiogenic heating is taken into account, which is consistent with the geochemical inference that the heat flow in the Mesozoic-Cenozoic could be >90 mw/m 2 in the eastern NCC [Menzies and Xu, 1998; Menzies et al., 2007]. The enhanced heat flux due to the lithospheric instabilities remains similarly high for the first 150 Myr following the onset of the instability, but decreases thereafter (Figure 4b). The instability-induced heat flux depends on buoyancy number B (Figure 9b). Cratonic lithosphere with a smaller B has less chemical buoyancy, is easier to be destabilized and removed, and often leads to large heat fluxes (Figures 4 and 6). Observations show that the surface heat flux in the western stable block of NCC is mw/m 2 [Hu et al.,2000; Ren et al., 2007], while in the eastern NCC the averaged heat flux is ~65 mw/m 2 [Gong et al., 2011; Hu et al., 2000]. This suggests that the heat flux contrast at the surface is mw/m 2. Considering that the crust in WANG ET AL. HEAT FLUX AND TOPOGRAPHY CONSTRAINTS 3094

15 the western NCC is ~15 km or 50% thicker than in the eastern NCC (Figure 1a) [Li et al., 2014],theheatflux contrast at the Moho could be ~25-30 mw/m 2, assuming that the mantle heat flux for the western NCC is ~10 mw/m 2 as expected for ~200 km thick lithosphere and that the crustal heat production rate is the same for the western and eastern NCC. This estimated mantle heat flux contrast is quite consistent with that from our numerical models for B between 0.2 and 0.4 (Figure 9b) Residual Topography of the NCC Regions and Buoyancy Number B This study is the first effort to bring the residual topography to constrain the dynamical evolution of craton lithosphere. The residual topography is computed by subtracting crustal contribution from the observed topography (Figure 1c). We found that the eastern NCC region is on averaged m higher than the western NCC region, opposite to the trend in actual topography. Our numerical models show that topography contrast between the stable and destabilized lithosphere regions is sensitive to buoyancy number B and the reactivation process. This is because the topography contrast depends on the thermal and chemical buoyancy in the stable and destabilized lithosphere and the shallow mantle, which is heavily influenced by B. A smaller B (i.e., less chemical buoyancy for the cratonic lithosphere) makes the cratonic lithosphere easier to be removed, thins the thermal boundary layer more, and enhances the role of thermal buoyancy in surface topography. At B = 0.1, the topography contrast can be ~1.5 2km even 200 Myr following the onset (Figure 9a). For large B, the cratonic lithosphere is not as easy to be removed, and even after its removal, the cratonic lithospheric materials may rise back to the shallow depth due to their large chemical buoyancy. This tends to cause relatively small topography contrast. Our models demonstrate that B needs to be to produce the inferred m topography contrast between the western and eastern NCC regions (Figure 9a). This range of buoyancy number corresponds to a density difference of kg/m 3 between the cratonic lithosphere and the asthenosphere, which is generally consistent with the average density difference of kg/m 3 for cratonic mantle relative to primitive mantle estimated from other studies [Poudjom Djomani et al., 2001] Constraining Buoyancy Number B and Thermochemical Structure of NCC Lithosphere Combining the heat flux and residual topography constraints leads to an estimated buoyancy number B~ for the NCC cratonic lithosphere. This is also consistent with that inferred from magmatic activities. Wang et al. [2015] suggests that B needs to be larger than 0.3 in order to generate multistaged instabilities lasting for ~100 Myr. For B~ , a significant amount of cratonic lithospheric materials may exist in the top 200 km of the destabilized region including the lithosphere at ~200 Myr after the onset of instability, and these buoyant materials contribute to the elevated topography (Figure 3). This further suggests that 20% to 55% (or on average ~40%) of the original cratonic lithospheric materials may still exist in the top 200 km of the mantle including the lithosphere in the eastern NCC (Figure 10). Lithospheric thickness is estimated to be 80 km in the reactivated eastern NCC region but ~200 km in the stable western NCC region [Griffin etal., 1998; Menzies et al., 1993; Chen, 2009; Chen et al., 2008, 2009; Zhu et al., 2012a]. It has been proposed, based on geochemical observations, that the entire cratonic lithosphere of the eastern NCC, possibly including the lower crust, has been removed and replaced with the normal mantle that forms the new lithosphere [e.g., Gao et al., 2004]. However, some other geochemical studies suggest the co-existence of residual ancient refractory mantle and oceanic mantle in the eastern NCC regions [e.g., Xu et al., 2008; Wu et al.,2008;zheng et al., 2007, 2001]. The latter view is consistent with our results that ~40% of the original cratonic lithospheric materials may still exist in the top 200 km of the mantle below the eastern NCC region based on topography and heat flux constraints. How does the thermochemical structure from our models fit tothe seismically estimated lithospheric thickness for the eastern NCC region? It should be pointed out that the thermal lithosphere in our models is still relatively thin (~70 km) (Figure 10b), consistent with the seismic results. Some destabilized cratonic lithospheric materials return to the shallow depth due to their chemical buoyancy after they have descended to asthenosphere and thermally equilibrated there (e.g., Figure 3f) [Wang et al., 2015]. The destabilized cratonic lithospheric materials, if returned to very shallow depths, would become part of the newly formed lithosphere as they cool with time. However, some of the cratonic lithospheric materials may reside immediately below the lithosphere and stay at relatively high temperature (e.g., Figures 3f and 10b). Therefore, we propose that much of the cratonic lithosphere (up to ~50%) of the eastern NCC is not removed but effectively only stirred after the reactivation. WANG ET AL. HEAT FLUX AND TOPOGRAPHY CONSTRAINTS 3095