• Economic and Environmental Geology
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• v.49 no.4
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• pp.269-280
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• 2016

I presented three vector crustal magnetic anomaly components and six gradients by using spherical Slepian functions over the cap area of $20^{\circ}$ of radius centered on the South Pole. The Swarm mission, launched by European Space Agency(ESA) in November of 2013, was planned to put three satellites into the low-Earth orbits, two in parallel in East-West direction and one in cross-over of the higher altitude. This orbit configuration will make the gradient measurements possible in North-South direction, vertical direction, as well as E-W direction. The gravity satellites, such as GRACE and GOCE, have already implemented their gradient measurements for recovering the accurate gravity of the Earth and its temporal variation due to mass changes on the subsurface. However, the magnetic gradients have little been applied since Swarm launched. A localized magnetic modeling method is useful in taking an account for a region where data availability was limited or of interest was special. In particular, computation to get the localized solutions is much more efficient and it has an advantage of presenting high frequency anomaly features with numbers of solutions fewer than the global ones. Besides, these localized basis functions that were done by a linear transformation of the spherical harmonic functions, are orthogonal so that they can be used for power spectrum analysis by transforming the global spherical harmonic coefficients. I anticipate in scientific and technical progress in the localized modeling with the gradient measurements from Swarm and here will do discussion on the results of the localized solution to represent the three vector and six gradient anomalies over the Antarctic area from the synthetic data derived from a global solution of the spherical harmonics for the crustal magnetic anomalies of Swarm measurements.

• Journal for History of Mathematics
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• v.18 no.1
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• pp.85-92
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• 2005

We review the well known analogizes between variations and harmonic maps. Second section contains rapid summary of the harmonic maps. In the third section we establish some basic properties of the Laplacian on Sphere. In particular we compute its spectrum and eigenfunctions.

• Journal of Korean Society for Geospatial Information Science
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• v.22 no.3
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• pp.113-119
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• 2014

The positioning accuracy of GNSS surveys deteriorates due to various error factor, and many users sometimes ignore Phase Center Variation (PCV) of antennas. IGS provides an ANTEX file which contains PCV correction information to correct for PCVs. But it is not directly applicable because PCV correction information is provided at 5-degree intervals in the azimuth and elevation directions for the case of receiver antennas, and at 1-degree intervals in the nadir angle for the case of satellite antennas. So, we devised new and optimal ways of interpolating PCV in any desired line of sight to the GNSS satellite. We used spherical harmonics fitting methods in terms of the azimuth and elevation angle for interpolation, and found an optimal degree and order. It is shown that the best accuracy was obtained from the 8 by 8 spherical harmonics. If one requires lower burden on computing resources, the order and degree less than 8 could produce resonable accuracy except for 1st and 5th order.

• Proceedings of the Korean Information Science Society Conference
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• 2005.07b
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• pp.844-846
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• 2005

본 논문에서는 3차원 모델을 검색하기 위한 형태 기반 기술자를 추출하는 알고리즘을 제안한다. 제안하는 알고리즘은 모델의 기하학적인 특성을 고려하여 레이 캐스팅 샘플링과 구면조화함수를 이용하는 방법이다. 레이 캐스팅 기법은 모델의 외형을 고려한 적응적인 방법으로 샘플링 하여 기술자에 포함되는 형태 정보를 증가시켜 기술자의 식별성을 높인다. 또한 구면조화함수 계수 추출에서는 기하학적인 주파수 특성을 고려하여 적응적인 계수를 추출한다. 이 방법은 검색 성능에 영향을 미치지 않고 기술자를 조밀하고 간결하게 만든다. 최종적으로 두 방법을 결합함으로써 검색 엔진에서 이용 가능한 기술자를 생성한다. 실험 결과에서는 제안된 알고리즘의 성능이 기존 방법에 비해 약 $12.5\%$ 향상 된 것을 확인 할 수 있다.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.43 no.2 s.308
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• pp.72-80
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• 2006

In this paper, we propose a new descriptor for 3D model retrieval based on shape information. The proposed method consists of two steps including ray casting method and spherical harmonic function, considering geometric properties of model. In the ray casting method, an adaptive sampling is performed for external shape information. By increasing shape information included in the descriptor, we improve the discriminating power of the proposed descriptor. The coefficients of spherical harmonic function are adaptively calculated, considering geometric frequency characteristics. This makes the descriptor more compact and concise without decreasing the retrieval performance. By combining two methods, we achieve more improved retrieval results.

• Journal of the Korean earth science society
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• v.28 no.7
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• pp.936-946
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• 2007

Analytical geopotential field in balance with the sectoral mode (the first symmetric mode with respect to the equator) of the Rossby-Haurwitz wave on the inclined rotation axis was derived in presence of superrotation background flow. The balanced field was obtained by inverting the divergence equation with the time derivative being zero. The inversion consists of two steps, i.e., the evaluation of nonlinear forcing terms and the finding of analytical solutions based on the Poisson's equation. In the second step, the forcing terms in the from of Legendre function were readily inverted due to the fact that Legendre function is the eigenfunction of the spherical Laplacian operator, while other terms were solved either by introducing a trial function or by integrating the Legendre equation. The balanced field was found to be expressed with six zonal wavenumber components, and shown to be of asymmetric structure about the equator. In association with asymmetricity, the advantageous point of the balanced field as a validation method for the numerical model was addressed. In special cases where the strength of the background flow is a half of or exactly the same as the rotation rate of the Earth it was revealed that one of the zonal wavenumber components vanishes. The analytical balanced field was compared with the geopotential field which was obtained using a spherical harmonics spectral model. It was found that the normalized difference lied in the order of machine rounding, indicating the reliability of the analytical results. The stability of the sectoral mode of Rossby-Haurwitz wave and the associated balanced field was discussed, comparing with the flrst antisymmetric mode.

• Journal of the Korean earth science society
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• v.37 no.2
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• pp.107-116
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• 2016

Stability of the barotropic Rossby-Haurwitz wave is investigated using the numerical models on the global domain. The Rossby-Haurwitz wave under investigation is composed of the basic zonal flow of super-rotation and a finite amplitude spherical harmonic wave. The Rossby-Haurwitz wave is given as either steady or unsteady wave by adjusting the strength of the super-rotating zonal flow. Stability as well as the growth rate of the wave in the numerical simulation is determined by comparing the perturbation amplitude at two different time stages. Unstable modes of the Rossby-Haurwitz wave exhibited a horizontal structure composing of various zonal-wavenumber components. The vorticity perturbation for some modes showed a discontinuity around the area of weak flow, which was found robust regardless of the horizontal resolution of the model. Fourier finite element model was shown to generate the unstable mode in earlier stage of the time integration due to less accuracy compared to the spherical harmonic spectral model. Taking the overall accuracy of the models into consideration, the time by which the unstable mode begin to dominate over the spherical harmonic wave was estimated.

• Geophysics and Geophysical Exploration
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• v.14 no.2
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• pp.133-139
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• 2011

The largest terms in the solid Earth body tide calculation are second degree spherical harmonic components due to the moon or the sun, and they compose about 98 percent of total contribution. Each degree harmonics of the tidal perturbation should be evaluated through multiplication with distinct Love numbers or their combinations. Correct evaluation of these terms in gravity tide is considered with re-calculated Love numbers. Frequency dependence of Love numbers for spherical harmonic tide upon the order number is discussed. Tidal displacement and tidally induced deviation of the vertical are also evaluated. Essential concepts underlying the body tide calculation are briefly summarized.

• Economic and Environmental Geology
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• v.41 no.2
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• pp.211-217
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• 2008

The gravity anomalies that observed by ground and shipborne survey and calculated from GRACE satellite are combined by using spherical cap harmonic analysis (SCHA). In this study, ground gravity data from Korea Institute of Geoscience and Mineral Resource(KIGAM) and shipborne gravity data from National Ocean Research Institute(NORI) and Korea Ocean Research and Development institute(KORDI) were used. L-2 level GRACE Gravity Model (GGM02C) was also used for satellite gravity anomaly. The ground and shipborne surveyed data were combined and gridded using Krigging method with 0.05 degree interval and GRACE data were also gridded using the same method with 0.05 degree to harmonize with the resolution of SCHA that has coefficient up to 80. Generalized Minimal Residual(GMRES) inversion method was implemented for calculating the coefficients of SCHA using the gridded ground and satellite gravity anomalies that had 0 km and 50 km altitude, respectively. The results of inversion method showed good correlation of 0.950 and 0.995 with original ground and satellite data. The gravity anomaly using SCHA satisfies Laplace's equation, therefore, using these SCHA coefficients, gravity anomaly can be calculated at any altitude. In this study, gravity anomaly was calculated from 10 km to 60 km altitude and each altitude, very stable results were shown. The ground and shipborne gravity data that have higher resolution and satellite data in long wavelength are harmonized well with SCHA coefficients and successfully applied in South Korea area. If more continuous survey and muti-altitude surveyed data like airborne data available, more precise gravity anomaly can be acquired using SCHA method.

• Journal of the Korean earth science society
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• v.32 no.6
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• pp.586-594
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• 2011

Gravity Recovery and Climate Experiment (GRACE), launched in April, 2002, makes it possible to monitor Earth's mass redistribution with its time-varying gravity observation. GRACE provides monthly gravity solutions as coefficients of spherical harmonics, and thus ones need to convert the gravity spectrum to gravity grids (or mass grids) via the spherical harmonics. GRACE gravity solutions, however, include spatial alias error as well as noise, which requires to suppress in order to enhance signal to noise ratio. In this study, we present the GRACE data processing procedures and introduce some applications of time-varying gravity, which are studies of terrestrial water storage changes, Antarctic and Greenland ice melting, and sea level rise. Satellite missions such as GRACE will continue up to early 2020, and they are expected to be an essential resource to understand the global climate changes.