ALBERT

Description: The influence of changes in surface ice-mass redistribution and associated viscoelastic response of the Earth, known as glacial isostatic adjustment (GIA), on the Earth's rotational dynamics has long been known. Equally important is the effect of the changes in the rotational dynamics on the viscoelastic deformation of the Earth. This signal, known as the rotational feedback, or more precisely, the rotational feedback on the sea level equation, has been mathematically described by the sea level equation extended for the term that is proportional to perturbation in the centrifugal potential and the second-degree tidal Love number. The perturbation in the centrifugal force due to changes in the Earth's rotational dynamics enters not only into the sea level equation, but also into the conservation law of linear momentum such that the internal viscoelastic force, the perturbation in the gravitational force and the perturbation in the centrifugal force are in balance. Adding the centrifugal-force perturbation to the linear-momentum balance creates an additional rotational feedback on the viscoelastic deformations of the Earth. We term this feedback mechanism, which is studied in this paper, as the rotational feedback on the linear-momentum balance. We extend both the time-domain method for modelling the GIA response of laterally heterogeneous earth models developed by Martinec and the traditional Laplace-domain method for modelling the GIA-induced rotational response to surface loading by considering the rotational feedback on linear-momentum balance. The correctness of the mathematical extensions of the methods is validated numerically by comparing the polar-motion response to the GIA process and the rotationally induced degree 2 and order 1 spherical harmonic component of the surface vertical displacement and gravity field. We present the difference between the case where the rotational feedback on linear-momentum balance is considered against that where it is not. Numerical simulations show that the resulting difference in radial displacement and sea level change between these situations since the Last Glacial Maximum reaches values of ±25 and ±1.8 m, respectively. Furthermore, the surface deformation pattern is modified by up to 10 per cent in areas of former or ongoing glaciation, but by up to 50 per cent at the bottom of the southern Indian ocean. This also results in the movement of coastlines during the last deglaciation to differ between the two cases due to the difference in the ocean loading, which is seen for instance in the area around Hudson Bay, Canada and along the Chinese, Australian or Argentinian coastlines.

Description: The downward continuation of the observed geomagnetic field from the Earth's surface to the core–mantle boundary (CMB) is complicated due to induction and diffusion processes in the electrically conducting Earth mantle, which modify the amplitudes and morphology of the geomagnetic field. Various methods have been developed to solve this problem, for example, the perturbation approach by Benton & Whaler, or the non-harmonic downward continuation by Ballani et al. In this paper, we present a new approach for determining the geomagnetic field at the CMB by reformulating the ill-posed, one-sided boundary-value problem with time-variable boundary-value function on the Earth's surface into an optimization problem for the boundary condition at the CMB. The reformulated well-posed problem is solved by a conjugate gradient technique using the adjoint gradient of a misfit. For this purpose, we formulate the geomagnetic adjoint-state equations for efficient computations of the misfit gradient. Beside the theoretical description of the new adjoint-state method (ASM), the first applications to a global geomagnetic field model are presented. The comparison with other methods demonstrates the capability of the new method to determine the geomagnetic field at the CMB and allows us to investigate the variability of the determined field with respect to the applied methods. This shows that it is necessary to apply the ASM when investigating the effect of the Earth's mantle conductivity because the difference between the results of approximate methods (harmonic downward continuation, perturbation approach) and the rigorous ASM are of the same order as the difference between the results of the ASM applied for different mantle conductivities.