16 research outputs found
The optimum expression for the gravitational potential of polyhedral bodies having a linearly varying density distribution
Gravitational field of the homogeneous rotational ellipsoidal body: a simple derivation and applications
Axially symmetric flow round a non-conducting obstacle in the shape of a hemisphere by a homogeneous electrical current field
Refraction of heat flow on subsurface contrast structures - the influence both on geothermal measurements and interpretation approaches
A model of returns for the post-credit-crunch reality: hybrid Brownian motion with price feedback
Cap integration in spectral gravity forward modelling: near- and far-zone gravity effects via Molodensky’s truncation coefficients
Spectral gravity forward modelling is a technique that converts a band-limited topography into its implied gravitational field. This conversion implicitly relies on global integration of topographic masses. In this paper, a modification of the spectral technique is presented that provides gravity effects induced only by the masses located inside or outside a spherical cap centred at the evaluation point. This is achieved by altitude-dependent Molodensky’s truncation coefficients, for which we provide infinite series expansions and recurrence relations with a fixed number of terms. Both representations are generalized for an arbitrary integer power of the topography and arbitrary radial derivative. Because of the altitude-dependency of the truncation coefficients, a straightforward synthesis of the near- and far-zone gravity effects at dense grids on irregular surfaces (e.g. the Earth’s topography) is computationally extremely demanding. However, we show that this task can be efficiently performed using an analytical continuation based on the gradient approach, provided that formulae for radial derivatives of the truncation coefficients are available. To demonstrate the new cap-modified spectral technique, we forward model the Earth’s degree-360 topography, obtaining near- and far-zone effects on gravity disturbances expanded up to degree 3600. The computation is carried out on the Earth’s surface and the results are validated against an independent spatial-domain Newtonian integration ((Formula presented.) RMS agreement). The new technique is expected to assist in mitigating the spectral filter problem of residual terrain modelling and in the efficient construction of full-scale global gravity maps of highest spatial resolution