Multi-physics adjoint modeling of Earth structure: combining gravimetric, seismic, and geodynamic inversions
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(2020) 11:30
ORIGINAL PAPER
Multi-physics adjoint modeling of Earth structure: combining gravimetric, seismic, and geodynamic inversions Georg S. Reuber1,2,3
· Frederik J. Simons4,5
Received: 30 July 2020 / Accepted: 23 October 2020 © The Author(s) 2020
Abstract We discuss the resolving power of three geophysical imaging and inversion techniques, and their combination, for the reconstruction of material parameters in the Earth’s subsurface. The governing equations are those of Newton and Poisson for gravitational problems, the acoustic wave equation under Hookean elasticity for seismology, and the geodynamics equations of Stokes for incompressible steady-state flow in the mantle. The observables are the gravitational potential, the seismic displacement, and the surface velocity, all measured at the surface. The inversion parameters of interest are the mass density, the acoustic wave speed, and the viscosity. These systems of partial differential equations and their adjoints were implemented in a single Python code using the finite-element library FeNICS. To investigate the shape of the cost functions, we present a grid search in the parameter space for three end-member geological settings: a falling block, a subduction zone, and a mantle plume. The performance of a gradient-based inversion for each single observable separately, and in combination, is presented. We furthermore investigate the performance of a shape-optimizing inverse method, when the material is known, and an inversion that inverts for the material parameters of an anomaly with known shape. Keywords Gravitational potential · Wave equation · Stokes equation · Adjoint-state method · Multi-physics inversion Mathematics Subject Classification 86-08
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Georg S. Reuber [email protected]
1
Institute of Geosciences, Johannes Gutenberg-University, Mainz 55128, Germany
2
Max-Planck Graduate Center, Mainz, Germany
3
Mainz Institute of Multiscale Modelling (M3ODEL), Johannes Gutenberg-University, 55128 Mainz, Germany
4
Department of Geosciences, Princeton University, Princeton, NJ 08544, USA
5
Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544, USA 0123456789().: V,-vol
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GEM - International Journal on Geomathematics
(2020) 11:30
1 Introduction Geophysics, both a systematic framework and a method for Earth exploration (Brown and Slawinski 2017) is traditionally divided into subdisciplines around distinct research methods, each focusing on a different observable, and making inferential statements about Earth properties through separate inversions for subsurface structure. In this paper we discuss the possibilities and advantages of conducting inversions that combine multiple physical observables in one single mathematical framework. 1.1 Forward and inverse problems in global geophysics All geophysics, like ancient Gaul, is divided into three parts, one of which is the domain of potential-field methods (gravity, geomagnetism, geo-electricity), the other that of seismic wave phenom
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