Efficient spatial-spectral computation of local planar gravimetric terrain corrections from high-resolution digital elevation models

Computation of gravimetric terrain corrections (TCs) is a numerical challenge, especially when using very high-resolution (say, ∼30 m or less) digital elevation models (DEMs). TC computations can use spatial or/and spectral techniques: Spatial domain methods are more exact but can be very time-consuming; the discrete/fast Fourier transform (D/FFT) implementation of a binomial expansion is efficient, but fails to achieve a convergent solution for terrain slopes >45°. We show that this condition must be satisfied for each and every computation-roving point pair in the whole integration domain, not just at or near the computation points. A combination of spatial and spectral methods has been advocated by some through dividing the integration domain into inner and outer zones, where the TC is computed from the superposition of analytical mass-prism integration and the D/FFT. However, there remain two unresolved issues with this combined approach: (1) deciding upon a radius that best separates the inner and outer zones and (2) analytical mass-prism integration in the inner zone remains time-consuming, particularly for high-resolution DEMs. This paper provides a solution by proposing: (1) three methods to define the radius separating the inner and outer zones and (2) a numerical solution for near-zone TC computations based on the trapezoidal and Simpson's rules that is sufficiently accurate w.r.t. the exact analytical solution, but which can reduce the computation time by almost 50 per cent

Development of a Synthetic Earth Gravity Model by 3D mass optimisation based on forward modelling

Several previous Synthetic Earth Gravity Model (SEGM) simulations are based on existing information about the Earth’s internal mass distribution. However, currently available information is insufficient to model the Earth’s anomalous gravity field on a global scale. The low-frequency information is missing when modelling only topography, bathymetry and crust (including the Mohorovičić discontinuity), but the inclusion of information on the mantle and core does not seem to significantly improve this situation. This paper presents a method to determine a more realistic SEGM by considering simulated 3D mass distributions within the upper mantle as a proxy for all unmodelled masses within the Earth.The aim is to improve an initial SEGM based on forward gravity modelling of the topography, bathymetry and crust such that the missing low-frequency information is now included. The simulated 3D mass distribution has been derived through an interactive and iterative mass model optimisation algorithm, which minimises geoid height differences with respect to a degree-360 spherical harmonic expansion of the EGM2008 global external gravity field model. We present the developed optimisation algorithm by applying it to the development of a global SEGM that gives a reasonably close fit to EGM2008, and certainly closer than a SEGM based only on the topography, bathymetry and crust

Mind Perception Is the Essence of Morality

Mind perception entails ascribing mental capacities to other entities, whereas moral judgment entails labeling entities as good or bad or actions as right or wrong. We suggest that mind perception is the essence of moral judgment. In particular, we suggest that moral judgment is rooted in a cognitive template of two perceived minds—a moral dyad of an intentional agent and a suffering moral patient. Diverse lines of research support dyadic morality. First, perceptions of mind are linked to moral judgments: dimensions of mind perception (agency and experience) map onto moral types (agents and patients), and deficits of mind perception correspond to difficulties with moral judgment. Second, not only are moral judgments sensitive to perceived agency and experience, but all moral transgressions are fundamentally understood as agency plus experienced suffering—that is, interpersonal harm—even ostensibly harmless acts such as purity violations. Third, dyadic morality uniquely accounts for the phenomena of dyadic completion (seeing agents in response to patients, and vice versa), and moral typecasting (characterizing others as either moral agents or moral patients). Discussion also explores how mind perception can unify morality across explanatory levels, how a dyadic template of morality may be developmentally acquired, and future directions

Assessment of a numerical method for computing the spherical harmonic coefficients of the gravitational potential of a constant density polyhedron

International audienceThis study focuses on the assessment of a linear algorithm for computing the spherical harmonic coefficients of the gravitational potential of a constant density polyhedron. The ability to compute such an expansion would favor several applications, in particular in the field of the interpretation and assessment of GOCE gravitational models. The studied algorithm is the only known method that would achieve this computation at a computational cost depending linearly on the number of computed coefficients. We show that although this methods suffers from severe divergence issues, it could be applied to retrieve band-limited estimates of the potential generated by a constant density polyhedron