Paleo-structure of the Earth's Mantle: Derivation from Fluid Dynamic Inverse Theory

Mantle convection is vital to our Earth system. The relentless deformation produced inside the Earth’s mantle by slow, viscous creep has a far greater impact on our planet than might be immediately evident. Continuously reshaping the Earth’s surface, mantle convection provides the enor mous driving forces necessary to support large-scale horizontal motion in the form of plate tectonics and the associated earthquake and mountainbuilding activity. At the same time, mantle convection induces substantial vertical motion in the form of topography dynamically maintained by lateral pressure gradients beneath tectonic plates. This vertical motion, on the order of 1 km or so, is perhaps the most spectacular manifestation of mantle convection—and its most enduring impact upon the entire Earth system. It is expressed ultimately on all scales—local, regional, global—through sea level variations and flooding events known from the geologic record to have reached deep into the interiors of continents (see Figure 1), with profound consequences for the opening and closure of marine pathways and their impact on the global climate system.The link between deep mantle processes and their surface manifestations is an issue of direct practical relevance, in particular concerning the evolution of sedimentary basins and their paramount economic importance in terms of hydrocarbon and other resources (see [4] for a recent review). The time scale of geologic processes, typically on the order of millions of years, is sufficiently long that the Earth’s mantle, although stronger than steel and capable of transmitting seismic shear waves, can be treated as a fluid. Mantle convection is thus governed by hydrodynamic field equations expressing the fundamental principles of mass, momentum, and energy conservation. Here, the form of the momentum equation is of particular interest. Because of the very high viscosity of the Earth’s mantle (in the range of 10 21 Pa·s), the momentum conservation law simplifies to the Stokes equation, where the inertia terms can be ignored owing to the negligible flow velocities (on the order of cm/year) and accelerations. The resulting instantaneous balance of frictional and buoyancy forces is represented by an elliptic partial differential equation, with driving forces for the flow arising from lateral density anomalies in the mantle. Time-dependence enters the mantle convection system through the energy equation, which describes the transport of heat inside the Earth’s mantle by advection and conduction. A rich spectrum of physics is compatible with the governing equations. Powerful computer models are available for simulating the mantle convection process (see [12] for a recent review), and software development now under way opens a path to exascale computing [3,8]. But grave uncertainties compromise our knowledge of crucial material parameters (temperature, composition, strength) in the mantle. In principle, it is possible to resolve these uncertainties by testing mantle convection models against data, such as paleo-shorelines or variations in the structure of sedimentary basins, gleaned from the geologic record. But geologic events—by definition—happened in the past. Modeling paleo-mantle convection currents so that they can be linked explicitly to the geologic record thus requires knowledge of the state of the convective system in the past, which, of course, is not available to us.