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  • 1.
    Abdollahzadeh, Makan
    et al.
    K.N.Toosi University of Technology, Faculty of Geodesy and Geomatic Engineering, Tehran, Iran.
    Eshagh, Mehdi
    KTH, Skolan för arkitektur och samhällsbyggnad (ABE), Transporter och samhällsekonomi (stängd 20110301), Geodesi (stängd 20110301).
    Najafi, Mehdi
    K.N.Toosi University of Technology, Faculty of Geodesy and Geomatic Engineering, Tehran, Iran.
    A semi-vectorization algorithm to synthesis of gravitational anomaly quantities on the Earth's surface2009Konferensbidrag (Refereegranskat)
    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.

  • 2.
    Abdollahzadeh, Makan
    et al.
    KTH, Skolan för arkitektur och samhällsbyggnad (ABE), Samhällsplanering och miljö, Geoinformatik och Geodesi.
    Najafi-Alamdari, Mehdi
    Geodesy, KNToosi Uni. Tech..
    Application of Molodensky's Method for Precise Determination of Geoid in Iran2011Ingår i: Journal of Geodetic Science, ISSN 2081-9919, E-ISSN 2081-9943, Vol. 1, nr 3, s. 259-270Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Determination of the geoid with a high accuracy is a challenging task among geodesists. Its precise determination is usually carried out by combining a global geopotential model with terrestrial gravity anomalies measured in the region of interest along with some topographic information. In this paper, Molodensky's approach is used for precise determination of height anomaly. To do this, optimum combination of global geopotential models with the validated terrestrial surface gravity anomalies and some deterministic modification schemes are investigated. Special attention is paid on the strict modelling of the geoidal height and height anomaly difference. The accuracy of the determined geoid is tested on the 513 points of Iranian height network the geoidal height of which are determined by the GPS observations.

  • 3.
    Eshagh, Mehdi
    et al.
    KTH, Skolan för arkitektur och samhällsbyggnad (ABE), Transporter och samhällsekonomi, Geodesi.
    Abdollahzadeh, Makan
    KTH, Skolan för arkitektur och samhällsbyggnad (ABE), Transporter och samhällsekonomi, Geodesi.
    Semi-vectorization: an efficient technique for synthesis and analysis of gravity gradiometry data2010Ingår i: EARTH SCI INFORM, ISSN 1865-0473, Vol. 3, nr 3, s. 149-158Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The harmonic synthesis and analysis of the elements of gravitational tensor can be done in few minutes if a suitable programming algorithm is used. Vectorization is an efficient technique for such processes, but the size of matrices will increase when the resolution of synthesis or analysis is high; say higher than 0.5 degrees x 0.5 degrees. Here, we present a technique to manage the computer memory and computational time by excluding one computational loop from the matrix products and we call this method semi-vectorization. Based on this technique, we synthesize the gravitational tensor using the EGM96 geopotential model and after that we analyze the tensor for recovering the geopotential coefficients. MATLAB codes are provided which are able to analyze 224 millions gradiometric data, corresponding to a global grid of 2.5' x 2.5' on a sphere in 1,093 s by a personal computer with 2 Gb RAM.

  • 4.
    Eshagh, Mehdi
    et al.
    KTH, Skolan för arkitektur och samhällsbyggnad (ABE), Samhällsplanering och miljö, Geoinformatik och Geodesi.
    Abdollahzadeh, Makan
    KTH, Skolan för arkitektur och samhällsbyggnad (ABE), Samhällsplanering och miljö, Geoinformatik och Geodesi.
    Software for generating gravity gradients using a geopotential model based on an irregular semivectorization algorithm2012Ingår i: Computers & Geosciences, ISSN 0098-3004, E-ISSN 1873-7803, Vol. 39, s. 152-160Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The spherical harmonic synthesis of second-order derivatives of geopotential is a task of major concern when the spatial resolution of synthesis is high and/or a high-resolution Earth's gravity model is used. Here, a computational technique is presented for such a process. The irregular semivectorization is introduced as a vectorization technique in which one loop is excluded from matrix-vector products of mathematical models in order to speed up the computation and manage the computer memory. The proposed technique has the capability of considering heights of computation points on a regular grid. MATLAB-based software is developed, which can be used for generating gravity gradients on an ordinary personal computer. The numerical results show that irregular semivectorization significantly reduces the computation time to 1 h for synthesis of these data with global coverage and resolution of 5′×5′ on an elevation model. In addition, a numerical example is presented for testing satellite gravity gradiometry data of the recent European Space Agency satellite mission, the gravity field and steady-state ocean circulation explorer (GOCE), using an Earth's gravity model.

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