• Geophysics and Geophysical Exploration
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• v.16 no.1
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• pp.59-62
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• 2013

We formerly reported a new method for the upward continuation of potential field on spherical patch area including Earth's curvature, which has been neglected in most studies on rectangular area with flat Earth assumption. This new method is applicable to downward continuation as well by only assigning corresponding value for the ratio of two radii; $r_2/r_1$, i.e., target radius $r_2$ versus datum radius $r_1$. In addition, the inherent problem of this method due to spherical surface geometry is described, and its one possible remedy is given.

• Economic and Environmental Geology
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• v.23 no.3
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• pp.353-358
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• 1990

This paper presents numerical experiments on migration of synthetic seismograms using by $45^{\circ}$ wave equation. The seismograms used are zero-offset seismogram (corresponding to stacked section) on point reflectors, dipping plane reflector, faulted and folded layers. The seismograms are constructed by upward continuation of seismic source wavelets, exploading on subsurface reflection interfaces, to the earth surface. The synthetic seismograms are migrated by downward continuation and imaging. The upward and downward continuations are implemented by solving the $45^{\circ}$ wave equation with the finite-difference method. Migration of the synthetic data used in this study results in relatively accurate reposition of subsurface structures while the synthetic sections are quite different from the structures.

• Economic and Environmental Geology
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• v.43 no.3
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• pp.249-258
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• 2010

In general, a crustal geomagnetic (or gravity) anomaly compiled at one altitude can be estimated at a different altitude by continuation using the Fourier transform (FT). However, in case of continuation with a great distance between the two elevations, or, in particular, in case of downward continuation, the estimated anomalies by the FT are likely to be mathematically unstable so that the estimated values are not realistic. To solve this problem, two independently measured magnetic field anomalies at different altitudes, such as aeromagnetic and satellite magnetic observations, are implemented to estimate values at in-between altitude for better understanding and interpreting geophysical and geological features. This ‘'dual continuation’' technique is straightforward in the FT and gives a more realistic estimate in all altitudes when we simulated with a set of prismatic bodies at different altitudes. This implies that we add up another constraint like satellite-based observations on the geopotential field modeling for the non-unique geological and geophysical problems to a conventional Fourier-type continuation technique with a single set of observations.

• 한국지구물리탐사학회:학술대회논문집
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• 2011.10a
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• pp.177-178
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• 2011

• Economic and Environmental Geology
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• v.14 no.2
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• pp.93-102
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• 1981

Studies of model potential fields continued upward and downward show differences depending on the method of continuation. Beginning with a magnetic field computed over a buried vertical cylinder, the field was continued to various levels by a method introduced by Henderson (Lagrangian interpolation) and by a spectral method (frequency domain analysis). Resultant fields show (1) no significant differences in upward continued values, (2) in downward continuation, accurate values are obtained with the spectral method over the central part of the anomaly, and (3) accurate values are obtained with Henderson's method on the flanks of the anomaly, while oscillations usually characterize the spectral method in this region. Essentially the same observations are made for derivative calculations. Field oscillations are empirically predicted at levels continued to approximately two-thirds of the depth of the source. Our spectral computer program output yields marked oscillations at one-half of the depth of the source. Henderson's method shows no oscillations at this depth and only minor oscillations at the top of the body (some negative values appear on the flanks of the anomaly). The Henderson output is a smooth field even if continued below the top of the body. These results suggest that the presence of oscillations cannot be used to identify the top of a buried source without careful consideration of the method used to continue the field. Use of the derivative to outline and isolate anomalies must similarly include consideration of the method of calculation.