Thermodynamics of continental deformation

Abstract

Continental deformation is known to be controlled by the interplay between tectonic and gravitational forces modulated by thermal relaxation-controlled lithospheric strength leading to oscillations around an equilibrium state, or to runaway extension. Using data-driven thermomechanical modelling of the Alpine Himalayan Collision Zone, we demonstrate how deviations from an equilibrium between mantle dynamics, plate-boundary forces, and the thermochemical configuration of the lithosphere control continental deformation. We quantify such balance between the internal energy of the plate and tectonic forces in terms of a critical crustal thickness, that match the global average of present-day continental crust. It follows that thicker intraplate domains than the critical crust (orogens) must undergo weakening due to their increased internal energy, and, in doing so, they dissipate the acquired energy within a diffused zone of deformation, unlike the localized deformation seen along plate boundaries. This evolution is controlled by a dissipative thermodynamic feedback loop between thermal and mechanical relaxation of the driving energy in the orogenic lithosphere. Exponentially growing energy states, leading to runaway extension are efficiently dampened by enhanced dissipation from radioactive heat sources. This ultimately drives orogens with their thickened radiogenic crust towards a final equilibrium state. Our results suggest a genetic link between the thermochemical state of the crust and the tectonic evolution of silicate Earth-like planets.

Figure 1

Long-term strength of the AHCZ. (a) Integrated strength of the crust and (b) of the lithosphere. Thermophysical and rheological parameters for the different geological layers are listed in Table 1 (see also “Methods”). Plate boundaries are plotted by green curves and earthquakes from ISC-GEM version 9 are overlaid by open circles, scaled by their magnitudes and colour-coded by their hypocentre depth (see legend in a). (c) Evolution of the integrated crustal strength as a function of its thickness for Mesozoic-Cenozoic tectonothermal ages, including oceanic regions. In (d) the crust with tectonothermal ages older than Mesozoic-Cenozoic is plotted. The size of the circles is scaled by the thickness of the upper crust (see legend in c) and colour-coded by the observed topography (see legend in d). In the background, white circles show the evolution of crustal strength vs thickness corresponding to a model where heat production in the crust is neglected (see Supplementary Fig. S2 online). Maps were made using Generic Mapping Tools Version 6.

Figure 2

Geoid anomaly, seismicity, and crustal configuration. (a) Crustal strength versus crustal thickness colour coded by the geoid height from ICGEM using the GECO model. In (b), the geoid height is filtered to a degree and order 10 (removing wavelengths higher than ~ 4000 km) to retain the signal from the upper mantle only. Note that the colour scale is centred at 0 m with red colours indicating positive values, and blue colours negative values. In the lower panels (c) and (d), earthquake epicentres at a given crustal thickness, are scaled by their hypocentre depths (≤ 80 km) (see legend in c) and colour-coded by their moment magnitudes (see legend in d). In (c) earthquakes with pure-thrust fault-plane solutions whereas in (d) earthquakes with pure-normal are plotted.

Figure 3

Stability and evolution dependence on energy parameter. Each panel shows the evolution of crustal thickness for possible initial states, also representing scenarios found in the major orogens of AHCZ. The black and grey curves denote experiments with initial state that resembles the lithosphere beneath Tibet and Alps, with no heat production in the crust, respectively. The orange curves illustrate the additional effect of considering surface processes (erosion and sedimentation) with a constant rate of 10 mm/yr. Note that there is only a slight difference by including surface processes, hence, orange curves overlay. Red curves consider the effect of heat production ($\mathrm{\chi }$ indicated in the panel title) for the perturbations equivalent to Tibet (thicker curves) and Alps (thinner curves). Similarly, the blue curves consider the additional effect of surface processes with a constant erosion and sedimentation rate of 10 mm/yr. Coloured dashed curves represent experiments where the initial state has been changed to sample other end-member perturbations. Each row represents an experiment with different $\mathrm{\psi }$ (see the row title), and each column with different creep activation energy, $\mathrm{\varphi }$, and HPE, $\mathrm{\chi }$ (see the column title). Decreasing the ratio of the thermal to viscous relaxation time, the run-away extensional states with no HPE, are attracted towards the equilibrium but take longer time (top to bottom). Decreasing the energy parameter leads to overall higher viscosities and lower strain-rate (Fig. 4), preventing these states from going to the run-away extension. Increasing the HPE and activation energy (left to right) increases the overall viscosity leading to dampening of the oscillations and shorter time to attain equilibrium crustal thickness.

Figure 4

Stability and evolution continental lithosphere. Viscosity evolution for different initial states corresponding to the crustal evolution in Fig. 3. Decreasing the ratio of the thermal to viscous relaxation time, the run-away extension states with no HPE, are attracted towards the equilibrium (top to bottom). Decreasing the energy parameter leads to overall higher viscosities and lower strain-rate, preventing these states from going to the run-away extension. Increasing the HPE and activation energy (left to right) increases the overall viscosity. Note that the experiments with $\mathrm{\psi }$=1000 (top row) show viscosities appropriate to the continental lithosphere.

Figure 5

Stability and evolution of the orogenic lithosphere. (a) Phase diagrams in crustal thickness-temperature space for orogen style perturbations (indicated by arrows) representing crustal thickness and temperatures found in the major orogens of AHCZ. The physical parameters are the same as in Figs. 3a and 4a. The black and grey curves denote experiments with initial state that resembles the lithosphere beneath Tibet and Alps, with no heat production in the crust, respectively. The orange curves illustrate the additional effect of considering surface processes (erosion and sedimentation) with a constant rate of 10 mm/yr. Note that there is only a slight difference by including surface processes, hence, orange curves overlay the black and grey curves. Red curves consider the effect of heat production (H of 1.0E−06 W/m³) for Tibet (thicker curves) and Alps (thinner curves) like states. Similarly, the blue curves consider the additional effect of surface processes with a constant erosion and sedimentation rate of 10 mm/yr. In (b)–(d) we only show time evolution of driving force, crustal thickness and mean lithospheric temperature corresponding to Tibet-type perturbation with (red curves) and without HPE (orange curves). In (b) total driving force evolution with time (solid red: with HPE) and contribution to it from thermal evolution (dashed red) of the system. Orange curve in (b) shows the evolution of total energy for a state with no HPE that shows runaway extension. In (c) and (d) we plot the corresponding evolution in time of the crustal thickness and mean lithospheric temperature, respectively. Open green and black circles in all the plots denote points where total force is zero within the first 200 Myr of the evolution referred to as metastable states. Paths marked as A and B represent key stages in the evolution of these experiments (see text for details).

Figure 6

Conceptual model for plate-tectonics. Schematic diagram depicting the evolution of an Earth-like planet in terms of its crustal thickness (h), crustal strength, and mantle potential temperature (T_p). The onset of plate tectonics is marked by point A after initial accretion (red domain to the left). The red curve denotes the secular cooling in terms of T_p (decreasing to the right), which controls the composition and thickness of the oceanic lithosphere (h_oc), thus setting a lower bound to the stability domain of mobile-lid plate tectonics. The dark green curve is the upper bound on crustal thickness growth during orogenesis, resulting from stresses imparted to the lithosphere from plate-boundary forces (PBF). The light green area in between represents the possible parameter space in terms of crustal thickness that may evolve in response to PBF and prevailing T_p. The dashed orange curve denotes the critical crustal thickness in equilibrium with PBF, as dictated by T_p and the internal energy of the crust. Point B represents the onset of a stable stagnant lid tectonic regime, in which subduction ceases, representing mechanical equilibrium between driving and resisting forces favouring thermal relaxation via diffusion. Point C denotes a stage of thermal equilibrium between the crust and mantle, marking tectonic quiescence. Any perturbation to the stable equilibrium state (black circle), such as thickening during orogenesis (orange diamond) or thinning (blue diamond), cause the system to evolve around this stable equilibrium state, the path of which is a function of the crustal rheology, composition, and internal energy content. The solid black arrows illustrate a typical evolutionary path from orogens to ocean lithosphere, whereas the dashed arrow indicates a system that goes towards runaway extension (rifting).