PUBLICATIONS Journal of Geophysical Research: Solid Earth RESEARCH ARTICLE 10.1002/2013JB010657 Key Points: • Craton destruction related to subduction is tested by numerical modeling • The overall thinning closely follows a natural log relationship over time • Combined convective erosion and peridotite-melt interaction cause destruction
Correspondence to: L. He,
[email protected]
Citation: He, L. (2014), Numerical modeling of convective erosion and peridotite-melt interaction in big mantle wedge: Implications for the destruction of the North China Craton, J. Geophys. Res. Solid Earth, 119, 3662–3677, doi:10.1002/2013JB010657. Received 2 SEP 2013 Accepted 21 MAR 2014 Accepted article online 26 MAR 2014 Published online 14 APR 2014
Numerical modeling of convective erosion and peridotite-melt interaction in big mantle wedge: Implications for the destruction of the North China Craton Lijuan He1 1
State Key Laboratory of Lithospheric Evolution, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, China
Abstract The deep subduction of the Pacific Plate underneath East Asia is thought to have played a key role in the destruction of the North China Craton (NCC). To test this hypothesis, this paper presents a new 2-D model that includes an initial stable equilibrated craton, the formation of a big mantle wedge (BMW), and erosion by vigorous mantle convection. The model shows that subduction alone cannot thin the cold solid craton, but it can form a low-viscosity BMW. The amount of convective erosion is directly proportional to viscosity within the BMW (η0bmw), and the rheological boundary layer thins linearly with decreasing log10(η0bmw), thereby contributing to an increase in heat flow at the lithospheric base. This model also differs from previous modeling in that the increase in heat flow decays linearly with t1/2, meaning that the overall thinning closely follows a natural log relationship over time. Nevertheless, convection alone can only cause a limited thinning due to a minor increase in basal heat flow. The lowering of melting temperature by peridotite-melt interaction can accelerate thinning during the early stages of this convection. The two combined actions can thin the craton significantly over tens of Myr. This modeling, combined with magmatism and heat flow data, indicates that the NCC evolution has involved four distinct stages: modification in the Jurassic by Pacific Plate subduction and BMW formation, destruction during the Early Cretaceous under combined convective erosion and peridotite-melt interaction, extension in the Late Cretaceous, and cooling since the late Cenozoic. 1. Introduction 1.1. Mechanisms of Craton Destruction From a geothermal point of view, areas of cratonic lithosphere are stable when surface heat flow (Qs) is in equilibrium with the heat supply at the base of the lithosphere plus the heat generated by radioactive decay within the lithosphere; any change in these terms can cause instability of the cratonic lithosphere. Thermal models [Michaut and Jaupart, 2007; Michaut et al., 2009] indicate that radiogenic heat production within the lithosphere is responsible for the long-term survival of the cratonic lithosphere, and a stable thermal structure requires that the average heat production within the lithospheric mantle does not exceed a critical value that is dependent on the thickness of the lithosphere. Mantle plumes can alter the heat flow at the base of the lithosphere, and the thermal effects of mantle plumes and associated lithospheric thinning have been modeled in previous studies [Davies, 1994; Ribe and Christensen, 1994; Sleep, 1994; Moore et al., 1999; Petitjean et al., 2006]. Moore et al. [1999] showed that plumes with excess temperatures of 100 to 200°C can efficiently thin the viscous lithosphere (over tens of Myr) by the formation of small-scale convective instabilities. However, Petitjean et al. [2006] demonstrated that at least 200 Myr is needed for a hot mantle plume (2000°C) to erode a thick solid region of lithospheric root. Subduction is an alternative way to disturb convective heat supply from below, although previous convection models have generally focused on the role of basal drag rather than thermal erosion [e.g., Artemieva and Mooney, 2002; Morency et al., 2002]. Currie and Hyndman [2006] suggested that uniformly thin, hot, and weak back-arc lithosphere is related to the shallow back-arc mantle flow that occurs during subduction. Widespread vigorous shallow convection, promoted by the release of water from the subducting slab, can also efficiently carry heat into the subduction zone region, causing elevated back-arc temperatures. Unfortunately, they only gave the conceptual model but did not provide the numerical results.
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1.2. Destruction of the North China Craton The NCC is a classic example of the destruction of an ancient craton [Menzies et al., 1993]. The NCC was stable from its formation until the Early Mesozoic; however, the mechanism that caused the destruction of this craton is controversial, with previous studies mainly advocating delamination [Deng et al., 1994, 2007; Gao et al., 2002, 2004; Wu et al., 2005] or thermal-chemical erosion [Fan and Menzies, 1992; Griffin et al., 1998; Fan et al., 2000; Xu, 2001; Zheng et al., 2006; Menzies et al., 2007]. However, a rapid delamination model cannot readily explain a long-lasting (~100 Myr) period of Mesozoic magmatic activity [Wu et al., 2008], and the traditional thermal erosion model is challenged by the fact that it requires both high temperatures (at least 100–200°C higher than asthenospheric temperatures) [Moore et al., 1999] and a long duration (>200 Myr) [Petitjean et al., 2006]. It should also be noted that no Mesozoic mantle plume has been documented to date in North China. Recent research has suggested that the destruction of the eastern NCC was closely linked to the subduction of the Pacific Plate underneath East Asia, starting in the Mesozoic [e.g., Zhao et al., 2007, 2009; Xu et al., 2009; Zhu and Zheng, 2009; Zhu et al., 2011, 2012a, 2012b]. The ancient Pacific Plate underwent rapid subduction (7–10 cm yr1), meaning that complete dehydration reactions may not have occurred at shallow depths (100–200 km) [Zhao et al., 2007]. A broad high-velocity anomaly has been identified within the mantle transition zone associated with this subduction. This anomaly is also associated with deep earthquake activity, suggesting that the Pacific slab is stagnating in this zone [Zhao et al., 2009]. Several hydrous minerals together with nominal anhydrous minerals within the cold subducting slab can accommodate and transport hydrogen into the transition zone [Komabayashi et al., 2004; Ohtani et al., 2004; Omori et al., 2004]. Richard et al. [2006] showed that coupled thermal and water diffusion in warming of the stagnant slab could produce local oversaturation of water in the slab, and the aqueous fluid can be generated by the slab dehydration in the overlying transition zone. The fluids formed in the transition zone tend to percolate into shallower depths [Ohtani and Zhao, 2009]; thereby, a big mantle wedge (BMW) is suggested to form that can extend for up to 1000 km from the Japan trench to East Asia [Lei and Zhao, 2005; Huang and Zhao, 2006; Zhao et al., 2007, 2009]. The addition of fluids in BMW may disturb mantle convection [Zhao et al., 2007; Chen, 2010] by reducing the mantle viscosity [Hirth and Kohlstedt, 2004]. The slab-derived fluids/melts, including carbonate, may also result in peridotite-melt interaction [Zhang, 2009]. Percolation of fluids/melts could cause drastic change of the wet solidus temperature of the mantle [Litasov and Ohtani, 2002; Litasov et al., 2011, 2013; Shatskiy et al., 2013]. Observations indicate that the source rocks of the strongly alkaline basalts in Shandong of the NCC were mainly carbonated peridotite [Zeng et al., 2010]. Fan et al. [2010] reported a new case of mantle-derived carbonate magma found in the Cenozoic basalts in Hannuoba and Yangyuan, NCC. The petrologic and geochemical signatures of the subcontinental lithospheric mantle (SCLM) modified by melt additions have been reflected by the basaltic rocks and deepseated xenoliths within the NCC [Tang et al., 2011, 2013]. Widespread melt-peridotite reactions within the SCLM that underlies the NCC may have been an important process associated with the destruction of the craton [Zhang, 2009; Tang et al., 2013]. Zhu et al. [2011, 2012a] proposed a conceptual model of the destruction of the NCC, whereby the subducted Pacific slab destabilized the mantle convection beneath the eastern NCC, leading to its destruction. This combined thermal erosion via vigorous mantle convection and peridotite-melt interaction may have resulted in significant thinning of the NCC lithosphere. This study focuses on the thinning of the cold solid craton above the BMW, using 2-D numerical modeling that incorporates a stable equilibrated craton, the formation of a BMW, and vigorous mantle convection. This research aims to identify the dynamic mechanisms involved in subduction-related convective erosion, quantify the thermal processes operating within the lithosphere, and identify the role (if any) of peridotitemelt interaction during lithospheric thinning. The results of this modeling shed light on the evolution of the NCC and can be used to test conceptual models of the destruction of the NCC.
2. Modeling Methodology The model employed in this study contains a solid lithosphere domain and a fluid asthenosphere domain (Figure 1). Following Petitjean et al. [2006], the bottom of the lithosphere (zl) is defined by an isotherm (e.g., 1200°C), and the viscosity of the model is infinite at temperatures lower than this isotherm.
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Figure 1. Setup of the numerical model used during this study. The model has a domain with a width of 2400 km, a depth of 650 km, and a crustal thickness of 40 km. The modeling involved three parts. (a) The thermal state of the stable craton is simulated to provide the initial conditions, as well as to provide a reference when comparing the periods before and after the destruction of the craton. (b) A subduction zone is added to simulate subduction and the formation of a big mantle wedge (BMW), with the aim of determining the thermal effects of subduction without considering dehydration. (c) The mantle viscosity is reduced in the BMW as a result of dehydration of stagnant subducted slab, forming vigorous mantle convection and causing thermal erosion of the lithosphere. This process is simulated by varying mantle viscosity values. The evolution of the cratonic lithosphere is also modeled by incorporating peridotite-melt interactions.
The asthenosphere (fluid mantle) is modeled as an incompressible Newtonian fluid, using the Boussinesq approximation and the following equations for convection: ∇ · u¼0 h i ∇ · PI þ η ∇u þ ð∇uÞT þ Δρg ¼ 0 ρcp
∂T þ ∇ ðk∇T Þ þ ρcp u ∇T ¼ A ∂t
(1) (2) (3)
where u, P, and T represent velocity, pressure, and temperature, respectively; t is time; η is mantle viscosity; g is acceleration due to gravity; cp is specific heat; k is thermal conductivity; A is radiogenic heat production; and Δρ defines a density anomaly, with Δρ = ρ0αΔT and α being the coefficient of thermal expansion. The solid lithosphere has a u value of 0, indicating that heat within the solid lithosphere is transferred entirely by conduction. The model assumes a temperature-dependent Newtonian rheology with η = η0 exp[E/R(1/T–1/Tb)], where E is the activation energy; η0 and Tb are background viscosity and background temperature within the upper mantle, respectively; and R is the gas constant. An E value of 120 kJ mol1 was used during modeling,
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Table 1. Parameters and Values Used During Modeling Parameter Background viscosity of asthenosphere Density at 0°C Reference temperature for density Cutoff temperature Boundary temperature of surface Gravity acceleration Thermal conductivity for crust Thermal conductivity for upper mantle Heat capacity Thermal expansion Radiogenic heat production of crust Radiogenic heat production of convective mantle Radiogenic heat production of conductive mantle
Symbol
Reference Value
η0 ρ T0
1 × 10 Pa s 3 3300 kg m 1200°C 1200°C 0°C 2 9.81 m s 1 1 2.5 W m K 1 1 3Wm K 1 1 1200 J kg K 5 1 3 × 10 °C 3 0.65 μW m 3 0.033 μW m 3 0 μW m
Tcutoff Tsurface g kc km Cp α Ac Am Alm
21
with a Tb value of 1350°C [Zhong and Watts, 2002]. The two-dimensional finite element modeling was undertaken using the commercial software Comsol Multiphysics (http://www.comsol.com/). The modeling involved three aspects as illustrated in Figure 1. First, both flow and temperature fields of the model are simulated until steady state is reached (Figure 1a). The thermal state of the stable craton is determined to provide the initial conditions, as well as to provide a reference when comparing the periods before and after the destruction of the craton. Second, a subduction plate boundary is added to simulate subduction and the formation of a big mantle wedge (BMW) (Figure 1b). The right boundary is changed to a temperature boundary, and the others keep unchanged. The model is remeshed. The aim of this part is to determine the thermal effects of subduction process alone without considering dehydration. Finally, the thinning processes of craton above BMW are modeled under the effects of convective erosion and peridotite-melt interaction. For simplicity, the complex process of dehydration is not incorporated into the modeling, and the effect of dehydration is considered by reducing the mantle viscosity. The mantle viscosity is reduced in the BMW as a result of dehydration of stagnant subducted slab, forming vigorous mantle convection and causing thermal erosion of the lithosphere (Figure 1c). This process is simulated by varying mantle viscosity values, and the cutoff temperature (Tcutoff ) between conduction and convection is maintained at 1200°C. At certain intervals during modeling (e.g., 510 Myr), the bottom of the lithosphere is recalculated depending on the isotherm of Tcutoff. In this modeling, the lithospheric base is treated as the interface between the solid and fluid domains. Accordingly, these two computational domains are reconstructed, and their meshes are recreated at given time steps. The evolution of the cratonic lithosphere is also modeled by indirectly incorporating peridotite-melt interactions through lowering of melting temperatures (Tmelt) of the lithosphere. But the melting processes are not taken into account in the models in order to simplify them. In the modeling, the cutoff temperature drops to reflect the lowering of Tmelt.
3. Initial Steady State Craton Previous numerical simulations have demonstrated that Archean cratonic lithosphere above convecting areas of the mantle is stable over long periods of time [Lenardic et al., 2003; Sleep, 2003; Petitjean et al., 2006]. The modeling undertaken during this study uses steady state lithosphere as the initial condition and as a reference to compare the model before and after craton destruction. The model domain has a width of 2400 km and a depth of 650 km (Figure 1), with a crustal thickness of 40 km. The model also has a surface boundary temperature of 0°C, with all other boundaries being insulating. The lower boundary of the model is an impermeable free-slip boundary with a value of (n · u = 0; t · [PI + η(∇u + (∇u)T )]n = 0); the other three boundaries of the fluid domain within the model are no slip (u = 0). The model is heated from within, and mantle heat production is confined to the convective mantle
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Temperature gradient (°C km-1) Figure 2. Steady state distribution of (a) temperature and (b) temperature gradient. Arrows indicate fluid flow directions, and solid white lines indicate the 1100°C, 1200°C, and 1300°C isotherms. (c) Vertical profiles showing variations in temperature Ts (z) (blue line) and temperature gradient (red line). (d) Profiles showing the upwelling rate and mantle viscosity; RBL = rheological boundary layer.
(i.e., no radiogenic heat production within the conductive mantle), generating a mantle heat flow of 15 mW m2. The crustal heat production within the model uses a mean value for the stable area of the western NCC (0.65 μW/m3) [Chi and Yan, 1998], and a mantle viscosity η0 of 1021 Pa s is based on postglacial rebound studies [Turcotte and Schubert, 2002]; all other parameters are listed in Table 1. The Rayleigh number (Ra) for a fluid layer heated from within is defined as Ra ¼
αgAm H5 C p ηκ2
(4)
where H is the thickness of the asthenosphere. The values given in Table 1 yield a Ra value of ~3 × 105, much greater than the minimum critical value Racr and indicating that convection will occur [Turcotte and Schubert, 2002]. A random temperature field was initially imposed in the convective mantle within the model, and density variations caused by thermal expansion generated buoyancy forces that drove thermal convection. After a few Gyr, both flow and thermal fields became steady (Figure 2), with a solid lithosphere some ~190 km thick. Thus, the model initial values of the lithospheric base (zl0) and surface heat flow (Qs0) are 190 km and 41 mW m2, respectively, consistent with estimates for the NCC during the Paleozoic [Xu, 2001; Wu et al., 2008]. The fact that the model does not include bottom heating means that only a top thermal boundary layer was generated, forming narrow zones of rapid downwelling and broad zones of slow upwelling (Figure 2a). The convective velocity reaches a maximum of 0.9 cm yr1 within the cold downwellings but is less than 0.3 cm yr1 in the upwelling zones of hot plume material (Figure 2d). Three layers can be distinguished from the steady geotherm (Figure 2c). First, a top layer represents the solid lithosphere. Heat within this layer is transported by conduction; consequently, this layer is termed the conductive boundary layer [Jaupart and Mareschal, 1999]. This layer does not participate in any convection (u = 0), and it has a temperature gradient that decays from ~16°C km1 at the surface to around 5°C km1 at the depth of the Moho, before maintaining a constant value within the solid mantle. Second, beneath this solid lithosphere layer is a ~130 km thick layer that is usually called the rheological boundary layer (RBL) [Sleep, 2003, 2006]. The temperature within this layer varies from 1200°C to 1550°C, and the temperature gradient decreases rapidly from top to bottom (Figure 2c). Within this region, heat is transferred by both conduction and convection. Finally, the bottom layer is the convective mantle. This layer has a low overall temperature gradient, and the viscosity of this layer decreases from the base of the lithosphere downward as a result of increasing temperature (Figure 2d).
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Figure 3. Changes in (a–e) temperature and (f–j) flow during subduction.
4. Subduction Process and BMW Formation The next stage of the modeling was the addition of a subduction plate boundary to simulate subduction until the formation of a BMW (Figure 1b). The initial values of temperature and fluid flow are those shown in Figure 2, but the right boundary of the model was changed to a temperature boundary, using the value of Ts (z) (Figure 2c). The subducting plate is assumed to initially dip at an angle of 45° and to subduct at a rate of u0 (7 cm yr1). The plate moves horizontally along the transition zone at depths of 650 km, and the conditions for the subducting slab and lower boundary are modified as follows: u0 ; s ≤ s0 slip; s > s0
(5)
where s0 is the subduction distance (s0 = t × u0) and s is the distance from the wedge tip. Other boundary conditions and parameters are unchanged from the previous model. The model was remeshed using triangle meshes, and the grids near the wedge tip were refined. The subducting plate reached a depth of 650 km at 9.3 Myr and then moved horizontally under the given conditions. Figure 3 shows variations in temperature and flow fields at different times in the modeling. Lithospheric temperatures are largely undisturbed by the viscous asthenosphere, and the base of the lithosphere remained unchanged. This indicates that subduction without dehydration cannot result in thinning of a cold, solid region of cratonic lithosphere. However, subduction does enable the formation of a low-viscosity BMW, with subduction causing a change in flow pattern and forming strong wedge flow within the BMW. The flow cell consists of a downgoing flow above the subducting slab and a return flow zone toward the corner of the mantle wedge corner. This flow pattern directly controls the area affected by fluids liberated by dehydration. Previous experimental studies have suggested that the downgoing slab and surrounding upper mantle transition zone (MTZ) contain water [e.g., Karato, 2011]. In addition, seismic studies have indicated that the
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Figure 4. Distribution of temperature and temperature gradient at η0bmw = 10 Pa s. The fact that the background viscosity within the BMW is 2 orders of magnitude less than the viscosity of the normal asthenosphere means that mantle convection within the BMW is more vigorous than outside this area. This compresses the rheological boundary layer, resulting in an abnormally high temperature gradient beneath the lithosphere. Arrows indicate flow magnitude and direction.
entire MTZ beneath northeast China is characterized by low shear wave velocities and high Vp/Vs ratios, suggesting an H2O content of ~0.2–0.3 wt % above the 660 km discontinuity [Ye et al., 2011]. High concentrations of water can decrease mantle viscosity by several orders of magnitude [Billen and Gurnis, 2001]. In addition, subduction zones are characterized by low mantle viscosities [Wang et al., 2012]. The flow distribution within the present model at 15 Myr indicates that it is possible to form a low-viscosity BMW that extends horizontally over more than 1000 km (Figure 3j).
5. Modeling Results of Craton Thinning Processes In this section, I successively model the thinning process of craton above BMW under the effects of convective erosion and peridotite-melt interaction. The effects of convective erosion due to dehydration are tested by reducing of the mantle viscosity and peridotite-melt interaction by lowering of melting temperature of the lithosphere. The model restarts from the position shown in Figure 3j, although the right-hand domains of the subducting boundary are not included in the calculations undertaken during this phase of modeling (i.e., they are set as inactive domains). The boundary conditions are identical to those outlined in section 3. 5.1. Role of Mantle Viscosity If the effect of dehydration on the mantle viscosity is ignored, mantle convection will gradually return to a steady state after subduction. However, if dehydration is considered, a change in mantle wedge viscosity
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Figure 5. (a) Vertical temperature and temperature gradient profiles for the area above the stagnant slab (η0bmw = 10 (b) Heat flow distribution within the lithosphere.
Pa s).
from 10 to 1000 times lower than the asthenosphere could trigger vigorous mantle convection. Dehydration of a subducting slab is complex and includes dehydration during subduction and dehydration of stagnated slab. However, this paper focuses on long-term convective erosion within the BMW, rather than the complex processes involved in slab dehydration. The effect of dehydration is indirectly implied by reducing the mantle viscosity. As such, the modeling presented here assumes that the mantle viscosity within the BMW is changed completely once formed. A η0bmw value of 1019 Pa s was firstly used to describe in detail the transient process of lithospheric thinning, and the base of the lithosphere was recalculated depending on the depth of the 1200°C isotherm at certain intervals during modeling (e.g., 510 Myr). Accompanied by the adjustment of the lithospheric base, the geometries of both solid and fluid domains are redrawn and remeshed. The decreasing viscosity causes an increase in Ra values, leading to more vigorous convection within the BMW (Figures 4a–4f ). The top of the asthenosphere has a temperature of ~1550°C, and it moves upward within the first 10–20 Myr of modeling. This causes significant compression of the RBL from an initial thickness of ~130 km to ~40 km (Figure 5a). The temperature gradient within this layer increases significantly, up to a maximum of 17°C km1 (Figure 5a), forming a thin layer with an anomalously high thermal gradient immediately beneath the lithosphere (Figures 4g–4l). Conductive heat flow at the base of the lithosphere (Qb) increases from the original (Qb0) value of 15 to >30 mW m2. This indicates that the original thermal balance is broken, with mantle convection supplying more heat than can be removed by conduction of the lithosphere and causing thinning of the lithosphere by heating. This continuing erosion causes the lithosphere to become hotter, whereas the asthenosphere becomes colder. This causes a gradual decay in basal heat flow (Figures 5 and 6), with an initial heating of the lowermost part of the lithosphere (Figure 5). This ongoing upward heating causes the base of the lithosphere to migrate upward (Figures 4g–4l and 6a), and the majority of the lithospheric mantle is affected after 100 Myr has
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elapsed. The heat flow within the lithospheric mantle varies over a range of 15–30 mW m2, and the addition of more heat into the crust after this time drives the lithosphere to a new equilibrium. However, surface heat flow only increases slightly during this modeling (Figure 6c). The modeling results indicate that the time-dependent lithospheric thinning proceeds at a rate that may be as high as 0.6 km Myr1 during the first 20 Myr, before gradually declining.
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This modeling also constrained the influence of mantle viscosity on convective erosion and indicates that convective erosion is directly proportional to mantle viscosity. The thinning of the RBL from 58 to 22 km is coincident with a decrease in η0bmw from 1020 to 1018 Pa s; an additional linear relationship is also present between HRBL and log10 (η0bmw) (Figure 7g).
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Figure 6. (a) Temporal variations in the base of the lithosphere. (b) Temporal variations in mean lithospheric thickness and thinning rate. (c) Temporal var19 iations in surface and basal heat flow; η0bmw = 10 Pa s.
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log10(η0bmw) Figure 7. Variations in the RBL with changing η0bmw values. (a–f) Results of modeling (t = 60 Myr) for η0bmw values of 20 19 19 18 18 18 1 × 10 , 5 × 10 , 1 × 10 , 5 × 10 , 2 × 10 , and 1 × 10 Pa s, respectively. (g) Linear relationship between the thickness of RBL (HRBL) and log(η0bmw).
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Figure 8. Variations in (a) ΔQb and (d) ΔQs as a function of changes in t
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x 1/2
and can be fitted using ΔQb = B (t ) + A, where both the slope (B) and intercept (A) linearly correlate with log10(η0bmw). In 1/2 1/2 addition, (e and f) ΔQs is proportional to t and has a best fit line of ΔQs = D*(t ) + C, where D and C both linearly correlate with log10(η0bmw).
undertaken during this study shows that only limited increases in heat flow can be generated in this manner. Spohn and Schubert [1982] defined λ as λ = Qb/Qb0, indicating that λ values are generally less than 4 in this study. This is much lower than the values assumed by Spohn and Schubert [1982], although their modeling placed a plume beneath the lithosphere, yielding λ values of 1–50. The modeling undertaken during this study differs from that undertaken by Spohn and Schubert [1982] in that the latter study involved a constant basal heat flow, whereas the modeling discussed here employs heat flow increment ΔQb(= Qb Qb0) and ΔQs (= Qs Qs0) that decay linearly with t1/2 (Figure 8). A set of linear expressions can be obtained for ΔQb t1/2 and ΔQs t1/2; these are listed in Table 2. Theoretically, surface heat flow will be equivalent to the basal heat flow when a new equilibrium is reached; this indicates that the time (tequ) needed to regain equilibrium can be estimated by assuming ΔQb is equal to ΔQs. In addition, tequ values decrease with decreasing mantle viscosities, with a η0bmw value of 1018 Pa s occurring at a tequ of 352 Myr; once equilibrium is reached, the basal heat flow (Qbequ) and surface heat flow (Qsequ) is 24.2 mWm2 and 50.2 mWm2, respectively.
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Table 2. Linear Expressions for the Relationship Between Increases in Heat Flow and t Lithosphere Defined by the 1200°C Isotherm η0bmw (Pa s) 18
1 × 10 18 2 × 10 18 5 × 10 19 1 × 10 19 5 × 10 20 1 × 10
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1/2
352 366 390 493 521 577
1.324* t + 34.06 1/2 1.234* t + 31.01 1/2 1.003* t + 25.46 1/2 0.652* t + 19.18 1/2 0.34* t + 9.82 1/2 0.211* t + 6.42
1.017* t 9.89 1/2 0.799* t 7.79 1/2 0.570* t 5.60 1/2 0.382* t 3.77 1/2 0.164* t 1.69 1/2 0.102* t 1.10
©2014. American Geophysical Union. All Rights Reserved.
, With the Base of the
Qbequ
Qsequ
2
(mW m
24.2 22.4 20.7 18.3 17.1 16.3
)
2
(mW m
)
50.2 48.4 46.7 44.3 43.1 42.3
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1/2
Figure 9. Relative thinning of the lithosphere as a function of (a) (t/τ) and (d) t. (b and c) Δzl decreases linearly with the square root of time within a given period (τ = 150 Myr), where both the slope (B) and intercept (A) linearly correlate with log10(η0bmw). However, (e and f) the overall thinning process is best fitted using a natural logarithmic curve, where D and C both linearly correlate with log10(η0bmw).
Figure 9 shows the relative thinning of the lithosphere as a function of (t/τ)1/2, where τ is the time constant defined as τ = zl2/κ/π2, which yields a value of ~150 Myr in this study. The lithospheric thickness initially decreases with the square root of time but subsequently slows. This indicates that lithospheric thinning (Δzl) can be approximated using a natural logarithmic curve (Figure 9d). This contrasts with the results of Spohn and Schubert [1982], who documented that the lithosphere thins at a rate that is inversely proportional to the square root of time during a significant proportion of the time between the initial and final equilibrium states. Their modeling suggests that the square-root-of-time law is only invalid at states near equilibrium. This difference between the two studies is predominantly due to the constant basal heat flow used during their modeling, whereas basal heat flow decreases with t1/2 in the present study. The Δzl-t relationships and the final depth of the base of the lithosphere (zequ) are given in Table 3, and the final equilibrium thickness of the lithosphere is controlled by the mantle viscosity within the BMW. The modeling presented here yielded a final thickness of 111 km, even though the η0bmw value was lowered to 1018 Pa s. This suggests that the thermal erosion within the BMW cannot be the sole thinning mechanism for the destruction of a craton like the NCC. 5.2. Role of Melting Temperature The presence of H2O can also lower the melting temperature of mantle peridotite [Olafsson and Eggler, 1983]. The H2O-saturated solidus of a model mantle composition is determined to be Table 3. Relationships Between Lithospheric Thinning Over Time and the Final Lithospheric Thicknesses for Different Mantle Viscosities just above 1000°C at pressures of 5–11 GPa [Kawamoto and Holloway, 1997]. But deep η0bmw (Pa s) Δzl (km) zequ (km) dehydration of stagnant slab may not be 18 1 × 10 19.18*ln(t) 33.93 111 18 a major process of material transport 16.73*ln(t) 28.73 120 2 × 10 18 through above mantle or backflow along 5 × 10 14.64*ln(t) 26.84 129 19 12.52*ln(t) 25.23 138 1 × 10 the slab-mantle interface due to 19 5 × 10 7.60*ln(t) 17.90 160 significant solubility of hydrogen in 20 5.36*ln(t) 13.81 170 1 × 10 transition zone minerals [Litasov, 2011].
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Figure 10. Variations in lithospheric thickness and surface heat flow with time. The initial stages of modeling incorporate partial melting due to peridotite-melt interaction. This melting plays a key role in lithospheric thinning, although contemporaneous convective erosion also acts to thin the lithosphere. Lithospheric thinning slows down gradually after these initial stages, and a natural logarithmic curve can still reasonably approximate thinning as a function of time.
In addition to H2O, subducting plates can also yield other melting-related volatiles, including CO2. Compared to dehydration, the decarbonation of the slabs plays a more important role [Litasov, 2011]. Carbonatite melt ascents as buoyant diaper, modifying and oxidizing the upper mantle [Litasov et al., 2013]. Experiments show that the presence of carbonate phases depresses greatly the solidus temperature of mantle peridotite [e.g., Canil and Scarfe, 1990; Dalton and Presnall, 1998; Brey et al., 2008; Ghosh et al., 2009], and H2O-CO2-bearing peridotites may have much lower melting temperatures than normal peridotites [Litasov et al., 2011]. Widespread peridotite-melt interactions have been identified within the SCLM that underlies the NCC [Zhang, 2009; Tang et al., 2013]. This model does not directly incorporate the chemical process of the peridotite-melt interaction but pay attention to the lowering of Tmelt of the lithospheric mantle resulted by peridotite-melt interaction [Zhang, 2009]. In this section, Tmelt is regarded as the cutoff temperature between conduction and convection. According to the isotherm of Tmelt, the lithospheric bottom is recalculated, and both solid and fluid domains are adjusted and remeshed at certain intervals during modeling. This section describes modeling that incorporates assumed Tmelt of 1200–1000°C within the BMW, with a η0bmw value of 1019 Pa s and with all other parameters unchanged. This modeling indicates that the lithosphere thins rapidly as a result of combined lowering of both melting temperatures and viscosities (Figure 10). The initial period of modeling indicates that partial melting caused by peridotite-melt interaction
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Figure 11. Schematic illustration of the dynamic evolution of the NCC since the Mesozoic.
plays a key role in the thinning of the lithosphere, although simultaneous convective erosion also contributes to this process. This period is followed by a gradual decrease in the rate of lithospheric thinning, although a natural logarithmic curve can still reasonably approximate the thinning of the lithosphere over time. This modeling indicates that the lithosphere thins to 89 km over 200 Myr at a Tmelt value of 1000°C. Figure 10c shows changing surface heat flow over time; these results are similar to those discussed above, and the surface of the lithosphere only undergoes heating after 60 Myr. This increase in surface heat flow is small and lags behind the thinning of the lithosphere, yielding a value of 8 mWm2 after 200 Myr at a Tmelt value of 1000°C.
6. Conclusions and Implications for Destruction of the NCC The lithospheric thinning related to subduction, as modeled during this study, started with a stable equilibrated craton, followed by the formation of a BMW and the development of vigorous (upper) mantle convection. This modeling indicates that subduction alone cannot thin a cold solid craton, but it can cause the formation of a BMW. An increase in sublithospheric heat flow can be generated by compressing the RBL within the low-viscosity BMW, causing the system to move away from the original thermal equilibrium. The RBL thins in direct proportion to the decrease in log10(η0bmw) values, causing a limited increase in heat flow at the base of the lithosphere. This basal heat flow decays linearly with t1/2, and lithospheric thinning is approximated by a natural logarithmic relationship with time. The limited increase in heat flow means that convection within the low-viscosity BMW can thin a region of cratonic lithosphere, but this is not enough to destroy a craton. The lowering of melting temperature by peridotite-melt interaction can also accelerate the rate of early lithospheric thinning, and combined convective erosion and peridotite-melt interaction cause a significant thinning of the cratonic lithosphere over a short period of time. For example, modeling of a mantle viscosity of 1018–1019 Pa s and peridotite melting temperatures of 1000–1100°C indicates that the lithosphere could be significantly thinned over tens of Myr but at normal asthenospheric temperatures. This modeling provides insights into the Mesozoic destruction of the NCC. The modeling results, combined with the known magmatism and heat flow in the area, indicate that the post-Jurassic dynamic evolution of the NCC can be divided into four stages (Figure 11), as outlined below.
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First, Early Jurassic subduction of the Pacific Plate led to a region of slab stagnating beneath the NCC, forming a BMW. Little dehydration of the slab occurred during this stage of modeling, meaning that mantle viscosity only decreased slightly (perhaps 1019–1020 Pa s). Minimal magmatism occurred at 190–155 Ma, and these magmas were derived from an enriched region of the lithospheric mantle, producing rocks with negative εNd (t) values [Wu et al., 2005]. The limited nature of this magmatism was the result of the relatively thick and rigid lithosphere at this time, which prevented a high-degree partial melting and inhibited the migration of melts to the surface [Xu, 2001]. This thick and rigid lithosphere also prevented effective back-arc spreading and lithospheric extension. This first stage of destruction of the NCC was also characterized by rather weak convective erosion, causing the lithosphere to thin from 190 to ~170 km. This heating and erosion had no surficial expression barring local magmatism. The second stage of the destruction of the NCC occurred between the Late Jurassic and the Early Cretaceous and is characterized by a significant decrease in mantle viscosity to ~1018–1019 Pa s, associated with the ongoing dehydration of the stagnant slab. In addition, peridotite-melt interactions lowered the mantle peridotite melting temperature to 1000–1100°C. The vigorous convection during this stage resulted in rapid thinning of the lithosphere, associated with contemporaneous cratonic magmatism. Large-scale magmatism at 135–115 Ma has been identified within the NCC, and these magmas were derived from an enriched mantle source [Wu et al., 2005], although the enriched isotopic signature of these Early Cretaceous magmas implies a relatively thick lithosphere (>100 km). This suggests that the lithosphere could have thinned from 170 to 100–120 km during this stage. The entire lithosphere was becoming hotter and weaker relative to the cool and rigid ancient craton, meaning the entire NCC was becoming easier to deform. However, this significant erosion and magmatism was still associated with only a small increase in surface heat flow. During the third stage, slab rollback was initiated during the Late Cretaceous and was accompanied by extension of the thin and weak lithosphere and renewed magmatism [Sun et al., 2008]. The lithospheric thinning was dominated by extension rather than thermal erosion, and the lithosphere was thinned to ~65 km [Zhang, 2009], causing the upwelling of hot asthenospheric material and large-scale partial melting. This melting formed Cenozoic basalts that were erupted in extensional basins developed within the craton (e.g., Bohai Bay Basin). These basalts are characterized by positive εNd(t) values that are indicative of derivation from a depleted (asthenospheric) region of the mantle. This change in magmatism reflects the change in the processes that caused melting during thinning of the lithosphere [Xu, 2001; Xu et al., 2004, 2009]. The surface heat flow within the Bohai Bay Basin reached 7090 mWm2 during this stage, as evidenced by vitrinite reflectance and apatite fission track data [Hu et al., 2001]. The final stage of this evolution was characterized by thickening of the lithosphere to 80100 km, primarily as the result of thermal decay [Xu, 2001]. This final stage was accompanied by a gradual decrease in surface heat flow to present-day values of 61–64 mW m2 [He and Wang, 2003; Gong et al., 2011].
Acknowledgments This project was supported by the National Natural Science Foundation of China (91114202). I thank the Associate Editor and anonymous reviewers for their valuable comments and constructive suggestions that significantly improved the manuscript.
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