Tenzer & Bagherbandi ( 2012) rearranged formulae of the VMM (Vening-Meinesz Moritz) inversion problem (Meinesz 1931) for isostatic gravity disturbances. Wieczorek & Phillips ( 1998) modified Parker's formula (Parker 1973) from the Cartesian frequency domain into the spherical harmonic domain and applied it to the determination of the Moon's crustal thickness. Therefore, the most effective methods employ spherical coordinates. ( 2017).įor applications over large geographical areas, the Earth's curvature must be taken into consideration. Meanwhile, methods based on swarm intelligence have been introduced to solve the inversion problem by Zhan & Zhao ( 2010) and Pallero et al. ( 2006), Chakravarthi & Sundararajan ( 2007) and Chai & Hinze ( 1988) investigated inversion methods of an interface that has depth-dependent density variations and that yields superior results when dealing with the sedimentary rocks. The latter is based on the method proposed by Parker ( 1973) in the spectral domain. ( 1996) introduced forward and inverse methods of a density interface using the Parker–Oldenburg method (Oldenburg 1974). Guspí ( 1992) proposed a method of inverting for a density contrast using Fourier transforms. The inversion may be approached in either the spatial or spectral domains. The inversion problem is satisfied by determining depths of the prisms that can reproduce the observed gravitational data. Methods discussed in the literature generally use Cartesian or spherical coordinate systems.įor local studies, the surface undulation of the interface, for example, the basement depths of a sedimentary basin, is normally represented by a set of juxtaposed right-rectangular prisms. The determination of the geometry of the interface is approached as an inversion problem using the gravitational data. In general, the problem can be summarized as solving for the deviations of an objective interface that separates two media with respect to a reference surface. Such studies are important because they have significant implications for tectonic interpretations or regional estimates of isostasy. 2004 Bagherbandi 2012a, b Uieda & Barbosa 2017) or the estimation of the geometry of an arbitrarily shaped mass body (D'Urso 2015 D'Urso & Trotta 2017 Ren et al. 2006 Chakravarthi & Sundararajan 2007), determination of the Moho discontinuity (Zhang et al. Existing techniques have led to numerous applications such as the estimation of basement relief (Guspí 1992 Silva et al. The merits of the tessellation method prove to outweigh those of traditionally used semianalytic approaches, especially when it comes to generality and applicability.Lunar and planetary geodesy and gravity, Planetary interiors, Crustal structure, Planetary tectonics 1 INTRODUCTIONĪ classical problem in the analysis of gravitational data is the estimation of the geometric properties, usually depth and surface undulations, of an interface with a density contrast (Barbosa et al. It is verified that the numerical method presented is accurate and sufficiently stable to be applied to more general situations than presented in this paper. We ignore interfacial deformation due to capillary, electrostatic, or gravitational forces, but the method can be extended to take such effects into account. The theory and numerical scheme presented here are sufficiently general to handle nonconvex patchy colloids with arbitrary surface patterns characterized by a wetting angle, e.g., amphiphilicity. The merits of the tessellation method prove to outweigh those of traditionally used semianalytic approaches, especially when it comes to generality and applicability.ĪB - We present a numerical technique, namely, triangular tessellation, to calculate the free energy associated with the adsorption of a colloidal particle at a flat interface. N2 - We present a numerical technique, namely, triangular tessellation, to calculate the free energy associated with the adsorption of a colloidal particle at a flat interface. T2 - Towards nonconvex patterned colloids T1 - Triangular tessellation scheme for the adsorption free energy at the liquid-liquid interface
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