Restoration of the evolution of a plume, Numerical assessment of the compressible adjoint equations in geodynamics
Abstract
Seismic tomography has seen continuous improvements over the last decades, to the point that some recent studies have reached the resolution necessary to image mantle plumes. Seismic tomography, however, can only give us a snapshot of mantle convection. In order to understand the dynamics of mantle plumes and their role in global mantle convection, one needs to study their evolution in time.Unfortunately, there is a fundamental lack of knowledge about the past history of mantle convection in general. It is possible, however, to restore past mantle states by recasting mantle convection as an inverse problem. An elegant and efficient method to solve this geodynamic inverse problem is given by the adjoint method, which allows to restore the mantle state at some arbitrary time in the past. This result is achieved through the solution of the equations that govern mantle convection, together with an auxiliary set of equations, called adjoint equations.The adjoint equations in geodynamics have already been derived under the assumption of incompressible (Boussinesq) flow, but the applicability to the real Earth of this approximation is limited, as density increases by almost a factor of two from the surface to the core-mantle boundary. Here we introduce the compressible adjoint equations for the conservation equations in the anelastic-liquid approximation and use them in a synthetic test based on the twin experiment method, reconstructing the past evolution of a plume rising from the lower boundary layer.We focus on three simulations. A first, termed Compressible, assumes the compressible forward and adjoint equations, and represents the consistent means of including compressibility effects. A second, termed Mixed, applies the compressible forward equation, but ignores compressibility effects in the adjoint equations. A third simulation, termed Incompressible, neglects compressibility effects entirely in the forward and adjoint equations relative to the reference twin. The compressible and mixed formulations successfully restore earlier structure of the plume, while the incompressible formulation yields noticeable artifacts.Our results suggest the use of a compressible formulation, when applying the adjoint method to seismically derived mantle heterogeneity structure.
- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2016
- Bibcode:
- 2016AGUFMDI41B2627G
- Keywords:
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- 5430 Interiors;
- PLANETARY SCIENCES: SOLID SURFACE PLANETSDE: 8121 Dynamics: convection currents;
- and mantle plumes;
- TECTONOPHYSICSDE: 8124 Earth's interior: composition and state;
- TECTONOPHYSICSDE: 8147 Planetary interiors;
- TECTONOPHYSICS