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A semi-vectorization algorithm to synthesis of gravitational anomaly quantities on the Earth's surface
K.N.Toosi University of Technology, Faculty of Geodesy and Geomatic Engineering, Tehran, Iran.
KTH, School of Architecture and the Built Environment (ABE), Transport and Economics (closed 20110301), Geodesy (closed 20110301).
K.N.Toosi University of Technology, Faculty of Geodesy and Geomatic Engineering, Tehran, Iran.
2009 (English)Conference paper (Refereed)
Abstract [en]

The Earth’s gravitational potential can be expressed by the well-known spherical harmonic expansion. The computationaltime of summing up this expansion is an important practical issue which can be reduced by an efficientnumerical algorithm. This paper proposes such a method for block-wise synthesizing the anomaly quantities onthe Earth surface using vectorization.Fully-vectorization means transformation of the summations to the simple matrix and vector products. It is not apractical for the matrices with large dimensions. Here a semi-vectorization algorithm is proposed to avoid workingwith large vectors and matrices. It speeds up the computations by using one loop for the summation either ondegrees or on orders. The former is a good option to synthesize the anomaly quantities on the Earth surfaceconsidering a digital elevation model (DEM). This approach is more efficient than the two-step method whichcomputes the quantities on the reference ellipsoid and continues them upward to the Earth surface. The algorithmhas been coded in MATLAB which synthesizes a global grid of 50 x 50 (corresponding 9 million points) of gravityanomaly or geoid height using a geopotential model to degree 360 in 10000 seconds by an ordinary computer with2G RAM.

Place, publisher, year, edition, pages
National Category
Geosciences, Multidisciplinary
URN: urn:nbn:se:kth:diva-63315OAI: diva2:481974
EGU General Assembly 2009. Vienna, Austria, 19 – 24 April 2009
QC 20120127Available from: 2012-01-23 Created: 2012-01-23 Last updated: 2012-01-27Bibliographically approved

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Abdollahzadeh, MakanEshagh, Mehdi
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