• 한국지구물리탐사학회:학술대회논문집
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• 2006.06a
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• pp.161-166
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• 2006

Vertical gravity gradient measurement offers greater structural resolution and detectability than gravity alone. Practical difficulties of field measurement of vertical gravity gradient have raised questions of its accuracy and utility. But, modern automated gravimeter of $1\;{\mu}Gal$ sensitivity makes it easier to measure vertical gradient with required accuracy. It is particularly effective to engineering and environmental problems which target shallow subsurface structure. This paper attempts to apply the vertical gravity gradient technique to high resolution density mapping. The method was generally reviewed and numerical inverse modeling was executed for comparing with conventional gravity. And actual vertical gravity gradient data surveyed overt karstic cavity area at Muan was analysed and interpreted.

• Geophysics and Geophysical Exploration
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• v.23 no.1
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• pp.55-60
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• 2020

The closed-form expressions of gravity, magnetic, gravity gradient tensor, and magnetic gradient tensor due to a rectangular prism are derived. The vertical gravity is derived via triple integration of a rectangular prism in Cartesian coordinates, and the two horizontal components of vector gravity are then derived via cycle permutation of the axis variables of vertical gravity through the axial symmetry of the rectangular prism. The gravity gradient tensor is obtained by differentiating the vector gravity with respect to each coordinate. Using Poisson's relation, a vector magnetic field with constant magnetic direction can be obtained from the gravity gradient tensor. Finally, the magnetic gradient tensor is derived by differentiating the vector magnetic with respect to appropriate coordinates.

• Ocean and Polar Research
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• v.39 no.4
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• pp.257-267
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• 2017

Although Pacific mackerel (Scomber japonicus) is an important commercial species in Korea, its recruitment mechanism remains largely unknown. Diel vertical positioning of larvae in the water column, which is affected by their specific gravity and the surrounding water density, may help to provide an understanding on recruitment success through predator avoidance and prey availability. The specific gravity measurement on Pacific mackerel eggs and larvae would seem to be essential information necessary to learn about the transport process from spawning to nursery grounds, and consequently the recruitment success. Eggs were artificially fertilized, and larvae were fed with rotifer when their mouths opened 3-4 days after hatching. We conducted the experiment using a density gradient water column to measure the ontogenetic changes in specific gravity from fertilization to 10 days after hatching. Egg specific gravity was stable during most of the embryonic period, but a sudden increase to $1.0249g\;cm^{-3}$ happened just before hatching. However, the specific gravity of newly hatched larvae was much lighter ($1.0195g\;cm^{-3}$), and specific gravity tended to increase continuously after hatching. Comparison of specific gravity with seawater density reveals that eggs and newly hatched larvae can float in the surface layer of the ocean. For the later period of the experiment, the specific gravity showed a cyclic diel pattern: the highest in the evening while the lowest at dawn. The fullness of larval stomach may be responsible for the observed differences in specific gravity, because stomach fullness was lower (40-60%) at midnight, and higher (80-85%) in evening. The diel pattern of specific gravity might provide clues regarding how larvae match the diel vertical migration of prey organisms.

• Geophysics and Geophysical Exploration
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• v.26 no.1
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• pp.1-7
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• 2023

This study derives the expressions of vector gravity and gravity gradient tensor due to an elliptical cylinder. The vector gravity for an arbitrary three-dimensional (3D) body is obtained by differentiating the gravitational potential, including the triple integral, according to the shape of the body in each axis direction. The vector gravity of the 3D body with axial symmetry is integrated along the axial direction and reduced to a double integral. The complex Green's theorem using complex conjugates subsequently converts the double integral into a one-dimensional (1D) closed-line integral. Finally, the vector gravity due to the elliptical cylinder is derived using 1D numerical integration by parameterizing a boundary of the elliptical cross-section as a closed line. Similarly, the gravity gradient tensor due to the elliptical cylinder is second-order differentiated from the gravitational potential, including the triple integral, and integrated along the vertical axis direction reducing it to a double integral. Consequently, all the components of the gravity gradient tensor due to an elliptical cylinder are derived using complex Green's theorem as used in the case of vector gravity.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.51 no.3
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• pp.332-337
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• 2018

The Pacific cod Gadus macrocepahlus, lays demersal eggs and the hatching larvae rise toward the surface layer of the ocean to feed. The change in the specific gravity of eggs and larvae was investigated to examine their vertical distribution and movement in the water column. The specific gravities of fertilized eggs and various size classes of larvae were measured using a density gradient apparatus. In total, the instantaneous specific gravity of 146 eggs and 225 larvae were measured. To prevent any disturbance in the gradient water column due to larval movement, 0.004% MS222 was used for anesthesia. Due to their high specific gravity, eggs spawned were deposited over the sea-bed of the spawning ground. The specific gravity of hatching larvae decreased abruptly. However, Pacific cod larvae still had a comparatively high specific gravity at hatching ($1.03655{\pm}0.00146g/cm3$, n=4, mean SL=3.62 mm) and their specific gravities tended to decrease as they grew. The specific gravity stabilized 6 days after hatching ($1.02590{\pm}0.00212g/cm3$, n=15, mean SL=4.67 mm) and the cod larvae were eventually able to float in the water column.

• Geophysics and Geophysical Exploration
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• v.27 no.1
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• pp.51-56
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• 2024

In this paper, the vector gravity and gravity gradient tensor of an elliptical disk are derived. The vector gravity of an elliptical disk is defined by differentiating the gravitational potential due to the elliptical disk expressed by a double integral with respect to each axial direction. The vector gravity defined by the double integral is then transformed into a line integral of a closed curve along the elliptical disk boundary using the complex Green's theorem. Finally, vector gravity due to the elliptical disk is derived by 1D parametric numerical integration along the elliptical disk boundary. The xz, yz, zz components of the gravity gradient tensor due to the elliptical disk are obtained by differentiating the vector gravity with respect to vertical direction. The xx, yy, xy components are derived by differentiating the horizontal components of the vector gravity in the form of a double integral with respect to horizontal directions and then using the complex Green's theorem.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.46 no.6
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• pp.957-965
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• 2013

This study simulated the egg vertical distribution of mackerel Scomber japonicus in Korean waters using general numerical models. All eggs were spawned naturally by raising broodfishes (May-June 2013), and the egg specific gravity was measured by a density-gradient column. CTD surveys provided environmental data (e.g., temperature and salinity) in May near Jeju Island, Korea. The egg specific gravity during the early stages ranged from 1.0203-1.0211. In general, the fertilized eggs showed a gradual decline in egg specific gravity until full development of the main organs, with a sudden increase just before hatching. Modeled egg vertical distributions were influenced more by wind speed than by egg buoyancy and vertical structure of the sea water. During calm and normal wind speeds, the eggs were distributed from the surface to 25-m depths. Under strong wind conditions (three times higher than the normal speed), the egg concentration on the surface decreased, and the egg distributional depth was deeper (~50 m).

• Economic and Environmental Geology
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• v.27 no.5
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• pp.479-489
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• 1994

In this paper, the iterative least-squares inversion method is used to determine shapes and density contrasts of 2-D structures from the gravity data. The 2-D structures are represented by their cross-sections of N-sided polygons with density contrasts which are constant or varying with depth. Gravity data are calculated by theoretical formulas for the above structure models. The data are considered as observed ones and used for inversions. The inversions are performed by the following processes: I) polygon's vertices and density contrast are initially assumed, 2) gravity are calculated for the assumed model and error between the true (observed) and calculated gravity are determined, 3) new vertices and density contrast are determined from the error by using the damped least-squares inversion method, and 4) final model is determined when the error is very small. Results of this study show that the shape and density contrast of each model are accurately determined when the density contrast is constant or vertical density gradient is known. In case where the density gradient is unknown, the inversion gives incorrect results. But the shape and density gradient of the model are determined when the surface density contrast is known.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.14 no.2
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• pp.127-139
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• 1996

This paper presents a procedure to recover sea surface heights (SSH) and free-air (FA) gravity anomalies from dense satellite altimeter SSH data with enhanced accuracies over the full spectrum of the gravity field. A wavenumber correlation filtering (WCF) of co-linear SSH tracks is developed for the coherent signals of sub-surface geological masses. Orbital cross-over adjustments with bias parameters are applied to the filtered SSH data, which are then separated into two groups of ascending and descending tracks and gridded with tensioned splines. A directional sensitive filter (DSF) is developed to reduce residual errors in the orbital adjustments that appear as track patterned SSH. Finally, FA gravity anomalies can be obtained by the application of a gradient filter on a high resolution estimate of geoid undulations after subtracting dynamic sea surface topography (DSST) from the SSH. These procedures are applied to the Geosat Geodetic Mission (GM) data of the southern oceans in a test area of ca. $900km\;\times{1,200}\;km$ to resolve geoid undulations and FA gravity anomalies to wavelengths of-10 km and larger. Comparisons with gravity data from ship surveys, predictions by least squares collocation (LSC), and 2 versions of NOAA's predictions using vertical deflections illustrate the performance of this procedure for recovering all elements of the gravity spectrum. Statistics on differences between precise ship data and predicted FA gravity anomalies show a mean of 0.1 mgal, an RMS of 3.5 mgal, maximum differences of 10. 2 mgal and -18.6 mgal, and a correlation coefficient of 0.993 over four straight ship tracks of ca. 1,600 km where gravity changes over 150 mgals.

• 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.