Thermal Regime and Evolution of the Congo Basin as an Intracratonic Basin

Abstract

The Congo Basin (CB) lies over a thick (200–250 km) and cold lithosphere: we estimate the present-day surface heat-flow to 40 ± 5 mW m⁻², from the BHT temperatures, lithology and porosity recorded in two oil wells and in agreement with the only measurement in this area (44 mW m⁻²). This value is consistent with the thickness of the lithosphere inferred from seismic tomography, assuming stationary conditions. The paleo-thermal regimes can be constrained by additional information, such as the pressures and temperatures derived from kimberlites studies, the variations of vitrinite reflectance with burial or the reconstructed subsidence history. The pressures and the temperatures derived from kimberlites xenocrysts suggest that the conditions were similar for at least 120 Myr. The long-term subsidence can be interpreted by the thermal relaxation of a thick lithosphere after a Neo-Proterozoic rifting stage (ca. 700–635 Ma) with a thinning factor β = 1.4 and a possible reactivation during the Karoo period (ca. 320 Ma). Because the magnitude of the crustal thinning is small, the past thermal conditions throughout the Phanerozoic were probably not very different from the present-day. Additional short term variations (~20–40 Myr) of the subsidence are interpreted by dynamic subsidence or uplift caused by sublithospheric mantle instabilities at the transition between litho-spheres of different thicknesses. These short term variations should not be associated with significant thermal changes. In order to explain the observed maturation of the vitrinite as well as angular uncomformities on seismic lines, one should assume one or two stages of erosion in the basin, representing at least 4 km of removed material. Heat advection by hydrothermal or volcanic fluids can conversely reduce the magnitude of this erosion.

Appendices

Appendix 1: Thermal Model

The thermal evolution is described by the 1D heat equation:

$$ {\mathit{\partial}}_z\left[\lambda \left(z,t\right){\partial}_zT\right]+A\left(z,t\right)=\rho c\left(z,t\right){d}_tT $$

(12.3)

where λ(z, t) is the thermal conductivity at depth z and time t, ρc(z, t) is the specific heat per volume unit and A(z, t) is the heat production. This equation is solved numerically by a finite differences method initially developed by Lucazeau and Le Douaran (Lucazeau and Le Douaran 1985). We use a Lagrangian frame, which allows to describe more easily the sedimentation (by adding nodes), the erosion (by removing nodes) or compaction and extension (by changing the thickness of a cell). The initial conditions assume thermal equilibrium within a 200 km thick lithosphere, with a 40 km thick crust and a 10 km enriched radiogenic upper crust. The upper and and lower boundary conditions are fixed temperatures (20 and 1,350 °C). This corresponds to a surface heat-flow of 43 mW m^− 2 and a mantle heat-flow of 16 mW m^− 2 (i.e. the upper limit assumed for the north American craton).

The time-dependant equation is solved implicitly, which gives less precision but more stability. In a first stage, we consider the rifting of the lithosphere. Modelled strain rates are typically low and therefore temperatures do not increase significantly due to the upward advection of mantle material, as the mantle cools at the same time as it deforms. This reduces the degree of subsidence during the stretching phase. The strain rate $\dot{\varepsilon}$ is related to the thinning factor β by:

$$ \beta = exp\left(\dot{\varepsilon}\varDelta t\right) $$

(12.4)

The subsidence of the CB constrains the thinning of the crust to a maximum of about 1.4. If we assume that extension ranges from 700 to 630 Ma, the strain rate is of the order of 10⁻¹⁶ s ⁻¹.

1.1 Lithosphere Physical Properties

The thermal conductivity of the mantle includes a lattice component λ _I , which depends on temperature and pressure, and a radiative component λ _r :

$$ {\lambda}_I=4.13\sqrt{\frac{298}{T_{abs}}\left(1+0.032\left({3.2410}^{-5}\left(z-{z}_{crust}\right)+1.14\right)\right)} $$

(12.5)

$$ {\lambda}_r={3.6810}^{-10}{T}_{abs}^3 $$

(12.6)

These expressions are derived from a compilation of literature data (Jaupart and Mareschal 1999).

The thermal conductivity of the crust also depends on the temperature and the thermal conductivity λ ₀ measured in laboratory conditions (Durham et al. 1987):

$$ \lambda =2.264-\frac{618.2}{T_{abs}}+{\lambda}_0\left(\frac{355.6}{T_{abs}}-0.3025\right) $$

(12.7)

1.2 Isostasy

We assume Airy-type isostasy, with a constant weight per surface unit at a reference level Z _ref in the asthenosphere. The initial state provides the reference weight M ₀ assuming that elevation corresponds to the sea-level:

$$ {M}_0={\rho}_c{\displaystyle {\int}_0^c\left(1-\alpha T(z)\right) dz+{\rho}_m{\displaystyle {\int}_c^L\left(1-\alpha T(z)\right) dz+({Z}_{ref}-L){\rho}_{asth}}} $$

(12.8)

where α is the coefficient of thermal expansion, ρ _c and ρ _m the density of the crust and mantle in laboratory conditions, T _L the temperature at the base of the lithosphere and ρ _asth  = ρ _m (1 − αT _L ) the density of asthenosphere.

At each time, the weight M1 is calculated to estimate the subsidence S:

$$ S=\frac{M_1-{M}_0}{\rho_{asth}-{\rho}_w} $$

(12.9)

Sediment physical properties

The porosity varies with depth z:

$$ \phi (z)={\phi}_0 exp\left(\frac{-z}{z_c}\right) $$

(12.10)

where ϕ ₀ is the porosity at the surface and z _c the compaction length. The thickness of a cell varies accordingly:

$$ \varDelta z=\Delta {z}_0\frac{\left(1-{\phi}_0\right)}{\left(1-\phi (z)\right)} $$

(12.11)

where Δz and Δz ₀ are the compacted and decompacted thicknesses of a cell. The thermal conductivity follows a geometric mean in the model:

$$ {\lambda}_{bulk}={\lambda}_{water}^{\phi (z)}{\lambda}_{matrix}^{1-\phi (z)} $$

(12.12)

where λ _bulk is the bulk conductivity, λ _water  = 0.6 W m⁻¹ K⁻¹ is the conductivity of water, and λ _matrix is the conductivity of the rock matrix.

The density (and the specific volumetric heat) follow harmonic means:

$$ {\rho}_{bulk}={\rho}_{water}\phi (z)+{\rho}_{matrix}\left(1-\phi (z)\right) $$

(12.13)

where λ _bulk is the bulk density, λ _water is the density of water, and λ _matrix is the density of the rock matrix.

Appendix 2: Model of Lithospheric Instabilities

To understand how a change in lithosphere thickness at the margins of the Congo Basin will affect subsidence we form an idealised model of viscous flow within a 2-D Cartesian domain. We assume that deformation of the lithosphere and asthenosphere can be effectively captured as a Stokes flow with the Boussinesq approximation. The numerical model is as outlined in Armitage et al. (2008, 2013). The key equation is the momentum balance,

$$ -\frac{\partial {\tau}_{ij}}{\partial {x}_j}+\frac{\partial p}{\partial {x}_i}=\varDelta \rho g{\lambda}_i $$

(12.14)

where τ _ij is the deviatoric stress, p is pressure, g is gravity and λ _i is a unit vector in the vertical direction. The change in density, Δρ is a function of temperature and melt depletion, F,

$$ \frac{\varDelta \rho }{\rho_0}=\Delta {\rho}_T+\Delta {\rho}_F=\alpha T+\beta F $$

(12.15)

where ρ ₀ is the mantle density at the surface, α = 3.3 × 10⁻⁵ K⁻¹ is the thermal expansion coefficient and β is the coefficient for change in density due to melt depletion (see below). Melt depletion F is tracked by a parameter X, which is a hypothetical completely compatible trace element. The value of X increases from 1 as melting progresses. The trace element can be related to melt depletion, F, assuming that the melt and solid remain in equilibrium with each other, by a simple mass balance, F = (X − 1)/X . We can then base the initial density variation with depth due to melt depletion on density changes predicted from melting experiments of natural and model rocks. We assume that change in density is a linear function of the removal of melt (Equation 12.15). This allows for β to be calculated from a reference state of melt depletion (Scott 1992),

$$ \beta =\frac{\Delta {\rho}_{ref}{X}_{ref}}{\rho_0\left({X}_{ref}-1\right)} $$

(12.16)

where X _ref  = 1.3, which is equivalent to F = 23 %. From the melting of model fertile lherzolite compositions and estimates from natural rocks, complete clynopy-roxene removal occurs at melt depletion of 23 %. This is our reference state of melt depletion, and using Δρ_ref = 34 kg m⁻³ as estimated for Proterozoic lithosphere (Poudjom Djomani et al. 2001), β = 0.04.

We consider a simple temperature dependent diffusion creep that is a reasonable approximation for the deformation of the Earth based on geological observations (Watts and Zhong 2000). Viscosity is given by,

$$ \eta ={\eta}_0{\eta}_{ref} exp\left(\frac{E}{RT}\right) $$

(12.17)

where E = 120 kJmol⁻¹ (Watts and Zhong 2000). The scaling viscosity, η₀ to dimensionalise dimensionless viscosity, is set from the thermal Rayleigh number,

$$ Ra=\frac{\alpha g{\rho}_m\varDelta T{d}^3}{\kappa {\eta}_0}=4.877\times {10}^6 $$

(12.18)

where d = 700 km is the depth to the base of the model; κ = 10^− 6 m² s^− 1 is the thermal diffusivity and ΔT = 1,315 K is the temperature difference between the surface and depth d. Using this Rayleigh number, the scaling mantle viscosity is η₀ = 10₂₀ Pa s. Finally η_ref = 1.129, which is calculated from a reference state (T_ref = 1,588 K) such that viscosity η = 10₂₀ Pa s at 200 km depth. The relatively small activation energy is justified by the observation within numerical experiments that a larger activation energy would predict too large a flexural rigidity or too thick an elastic plate near sea-mounts (Watts and Zhong 2000). This rheology is an obvious simplification, but it allows us to explore the general behaviour of the upper mantle with a geologically reasonable viscosity structure.

Appendix 3: Calculation of R _o

The calculation of R _o is similar to previous studies based on the transformation rate of vitrinite (Burnham and Sweeney 1989; Ungerer 1990); it is assumed that the vitrinite transformation can be described by a set of N independent Arrhenius first-order kinetic reactions:

$$ \frac{d{x}_i}{dt}={A}_i exp\left(\frac{E_i}{R\ {T}_{abs}}\right){x}_i(t) $$

(12.19)

where $\frac{d{x}_i}{dt}$ is the rate of the ith reaction, A _i the Arrhenius frequency factor (s ⁻¹), E _i the activation energy (kcal/mole), R the gas constant (0.001987 kcal/mole K), T _abs the absolute temperature and x _i the initial hydrocarbon potential for the it h reaction (mg hydrocarbon/TOC). x _i (t) can be determined by integration of the previous equation:

$$ {x}_i(t)={x}_i\left({t}_0\right)\left(1-\mathit{\exp}\left(-{A}_iR\frac{T^2\mathit{\exp}\left(\frac{-{E}_i}{R{T}_{abs}}\right)+{T}_0^2\mathit{\exp}\left(\frac{-{E}_i}{R{T}_{0\ abs}}\right)}{E_i\frac{T-{T}_0}{t-{t}_0}}\right)\right) $$

(12.20)

We have used a spectrum of 15 reactions (46–74 kJ) to determine the transformation rate of vitrinite and then an empirical relationship for the conversion to R _o . The effect of pressure, which tends to decrease the R _o value for a given heating rate (Carr 1999), has not been included.