The use of height data in gravity field approximation by collocation

Abstract

The accuracy of a gravity field model depends on the amount of available data and on the variation of the gravity field. When topographic height data are available, for example, in the form of a digital terrain model, it is possible to smooth the gravity field on a local scale by removing the gravitational effects calculated from models of the topographic masses. In this way, significant improvements of the prediction results are obtained in mountainous areas. In this paper we describe methods for the calculation of such gravitational terrain effects, applicable in collocation approximation of the gravity field. The terrain effects on gravity field quantities such as gravity anomalies, deflections of the vertical, and geoid undulations are calculated using a system of rectangular prisms, representing either a quasi‐traditional model of the topography and the isostatic compensation or a residual terrain model, where only the deviation of the topography from a mean elevation surface is considered. To test the terrain reduction methods, numerical prediction experiments have been conducted in the mountainous White Sands area, New Mexico. From gravity anomalies spaced approximately 6 arc min apart, other known gravity anomalies and deflections of the vertical were predicted using collocation. When using terrain effects calculated on the basis of 0.5 × 0.5 arc min point heights, the rms errors decreased by a factor of nearly 3 to 1 arc sec for the deflections and 3–4 mGal for the gravity anomalies, quite insensitive to the actual type of terrain reduction used. The feasibility of using topographic reductions in collocation is thus effectively demonstrated.

Local Geoid Determination in Mountain Regions.

“…Thus isostatic reduction, pragmatically regarded as trend removal, is essential for the practical application of least-squares collocation in mountainous regions (Forsberg and Tscherning, 1981).…”

“…1) Relevant formulas can be found in (Forsberg and Tscherning, 1981) with references to (MacMillan, 1958, pp. 78-79) and (Jung, 1961, p. 167).…”

A comparison of robust polynomial fitting, global geopotential model and spectral analysis for regional–residual gravity field separation in the Doñana National Park (Spain)

“…180 181 182 C is the classical terrain correction, computed by rectangular prism 183 integration method, taking into account the resolution of the digital 184 elevation model (Forsberg and Tscherning, 1981), B is the Bouguer 185 correction:…”

Análisis y ajuste de modelos de geoide. Observación y cálculo de la red gravimétrica de tercer orden en la Provincia de Valencia

“…El geoide del centro Peninsular fue refinado teniendo en cuenta los efectos terreno gracias a un mejor modelo digital del terreno proporcionado por la Defense Mapping Agency Aerospace Center, utilizando la técnica del modelo residual del terreno (Forsberg et al 1981), (Gil 1993), , (Sevilla 1995 La primera determinación de un geoide gravimétrico en la Península Ibérica y regiones colindantes se obtuvo en 1994 utilizando la técnica clásica de resolución de la integral de Stokes (Sevilla 1994).…”

“…Si lo que pretendemos es predecir la cantidad con un modelo continental o regional, basado en la técnica eliminar-restaurar (Forsberg et al 1981), (Albertella et al 1994), , se procederá de la siguiente manera: 1) Definiremos una malla lo suficientemente amplia en la que también aplicaremos la técnica eliminar-restaurar. Esta malla tendrá un espaciado en latitud y longitud correspondiente con la resolución del modelo de geoide utilizado, en este caso particular se ha utilizado tanto para el modelo EGG97 como para el IBERGEO95 un mallado de 1.5 X 1.5 minutos sobre un área que va desde los 35º45' N a los 43º45' N en latitud y -9º30' W a 4º30' E en longitud (área sobre la que está determinado el modelo IBERGEO95), de esta forma aseguramos que el error cometido por el hecho de no considerar el total de la malla (error que se producirá únicamente en el caso del modelo EGG97) sea mínimo, y, por supuesto, mucho menor de 0.03 mgal.…”