| 1. |
- Abdollahzadeh, Makan, et al.
(författare)
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A semi-vectorization algorithm to synthesis of gravitational anomaly quantities on the Earth's surface
- 2009
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Konferensbidrag (refereegranskat)abstract
- 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.
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| 2. |
- Abdollahzadeh, Makan, 1982-, et al.
(författare)
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Application of Molodensky's Method for Precise Determination of Geoid in Iran
- 2011
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Ingår i: Journal of Geodetic Science. - Poland : Versita. - 2081-9919 .- 2081-9943. ; 1:3, s. 259-270
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 3. |
- Eshagh, Mehdi, et al.
(författare)
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Semi-vectorization : an efficient technique for synthesis and analysis of gravity gradiometry data
- 2010
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Ingår i: EARTH SCI INFORM. - : Springer Science and Business Media LLC. - 1865-0473. ; 3:3, s. 149-158
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 4. |
- Eshagh, Mehdi, 1977-, et al.
(författare)
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Simplification of geopotential perturbing force acting on a satellite
- 2008
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Ingår i: Artificial Satellites. - Warsaw : Versita. - 0208-841X .- 2083-6104. ; 43:2, s. 45-64
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Tidskriftsartikel (refereegranskat)abstract
- One of the aspects of geopotential models is orbit integration of satellites. The geopotential acceleration has the largest influence on a satellite with respect to the other perturbing forces. The equation of motion of satellites is a second-order vector differential equation. These equations are further simplified and developed in this study based on the geopotential force. This new expression is much simpler than the traditional one as it does not derivatives of the associated Legendre functions and the transformations are included in the equations. The maximum degree and order of the geopotential harmonic expansion must be selected prior to the orbit integration purposes. The values of the maximum degree and order of these coefficients depend directly on the satellite's altitude. In this article, behaviour of orbital elements of recent geopotential satellites, such as CHAMP, GRACE and GOCE is considered with respect to the different degree and order of geopotential coefficients. In this case, the maximum degree 116, 109 and 175 were derived for the Earth gravitational field in short arc orbit integration of the CHAMP, GRACE and GOCE, respectively considering millimeter level in perturbations.
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| 5. |
- Eshagh, Mehdi, et al.
(författare)
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Software for generating gravity gradients using a geopotential model based on an irregular semivectorization algorithm
- 2012
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Ingår i: Computers & Geosciences. - The Netherlands : Elsevier. - 0098-3004 .- 1873-7803. ; 39, s. 152-160
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Tidskriftsartikel (refereegranskat)abstract
- 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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