• 한국지구물리탐사학회:학술대회논문집
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• 2003.11a
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• pp.459-463
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• 2003

Waveform inversion requires extracting a reliable low frequency content of seismic data for estimating of the low wave number velocity model. The low frequency content of the seismic data is usually discarded or neglected because of the band-limited response of the source and the receivers. In this study, however small the spectral of the low frequency seismic data is, we assume that it is possible to extract a reliable phase information of the low frequency from the seismic data and use it in waveform inversion. To this end, we exploit the frequency domain finite element modeling and source-receiver reciprocity to calculate the $Frech\`{e}t$ derivative of the phase of the seismic data with respect to the earth model parameter such as velocity, and then apply a damped least squares method to invert the phase of the seismic data. Through numerical example, we will attempt to demonstrate the feasibility of our method in estimating the correct velocity model for prestack depth migration.

• Geophysics and Geophysical Exploration
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• v.10 no.2
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• pp.138-146
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• 2007

This paper describes 2.5D induced polarization (IP) modeling and inversion algorithms using complex resistivity. The complex resistivity method has merits for acquiring more valuable information about hydraulic parameters and pore fluid than the conventional IP methods. The IP modeling and inversion algorithms are developed by allowing complex arithmetic in existing DC modeling and inversion algorithms. The IP modeling and inversion algorithms use a 2.5D DC finite-element algorithm and a damped least-squares method with smoothness constraints, respectively. The accuracy of the IP modeling algorithm is verified by comparing its responses of two synthetic models with two different approaches: linear filtering for a three-layer model and an integral equation method for a 3D model. Results from these methods are well matched to each other. The inversion algorithm is validated by a synthetic example which has two anomalous bodies, one is more conductive but non-polarizable than the background, and the other is polarizable but has the same resistivity as the background. From the inverted section, we can cleary identify each anomalous body with different locations. Furthermore, in order to verify its efficiency to the real filed example, we apply the inversion algorithm to another three-layer model which includes phase anomaly in the second layer.

• Korean Journal of Optics and Photonics
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• v.6 no.3
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• pp.178-187
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• 1995

The method that determines the appropriate damping factor is studied for a lens design. When suitable damping factor is applied to the additive damped least-squares (DLS) method, the convergence and the stability of the optimization process are examined in a triplet-type photographic lens design. We calculate eigenvalues of the product of the Jacobian matrix of error functions by using the singular value decomposition (SVD) method. We adopt the median of eigenvalues as an appropriate damping factor. The convergence and the stability of the optimization process are improved by choosing the adequate damping factor for the optimization of a photographic lens. It is known that the numerical inaccuracy in the calculation of normal equation is overcome by using the orthogonal transformations of the Jacobian matrix. Therefore, a combination of the method for setting a proper damping factor and the orthogonal transformations of the Jacobian matrix is good for application to the design of an aspheric lens with high-order terms. terms.

• Economic and Environmental Geology
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• v.28 no.5
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• pp.481-485
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• 1995

This paper presents a new approaching method to determine the velocity and geometry of shallow subsurface from seismic refraction events. After picking the first breaks from seismic refraction data, we assume that field refraction seismogram can be replaced by the unit delta function having time shift of first break. Time curves are generated by shooting ray tracing. The partial derivatives seismogram for a damped least squares method is computed analytically at each step of the forward ray tracing. The technique is successfully tested on synthetic and real data. It has the advantage of real full waveform inversion, which is robust at low frequency band even if the initial guess is far from the true model.

• Korean Journal of Optics and Photonics
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• v.12 no.2
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• pp.109-114
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• 2001

Optical system has some optical and mechanical constraints. The constraints should be preserved in optimization of optical system. For the purpose, the constraints are combined with the merit function by using Lagrange's undetermined multipliers. We propose an active optimization control by using the fact that the errors of constraints are corrected with higher priority than the other errors of the merit function. In this control, the errors which have large contribution to the merit function are converted into constraints. At that time, if the errors are corrected at once, the optimization will be unstable because of their non-linearity. Hence we introduce a target rate which represents a fraction of error to be corrected, and the errors are corrected progressively. An optimization program was developed on the bases of the proposed active control, and applied to design a photographic lens system. By using the active control, we could get better results compared with conventional damped least squares method. ethod.

• Geophysics and Geophysical Exploration
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• v.17 no.1
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• pp.11-20
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• 2014

To reveal shear-wave velocities ($v_s$) and site characterization of Wonju, Korea, Rayleigh waves were recorded at 78 sites of lower altitude using 12 to 24 4.5-Hz vertical geophones for 20 days during the period of February to September 2013. Dispersion curves of the Rayleigh waves obtained by the extended spatial autocorrelation method were inverted using the damped least-squares method to derive $v_s$ models. From these 1-D models, the average $v_s$ to a depth of 30 m ($v_s30$), $v_s$ of weathered rocks, depths to these basement rocks, and average $v_s$ of the overburden layer were derived to be $16.3{\pm}0.7m$, $576{\pm}8m/s$, $290{\pm}7m/s$, and $418{\pm}13m/s$, respectively, in the 95% confidence range. To determine adequate proxies for $v_s30$, we computed correlation coefficients of $v_s30$ with topographic slope (r = 0.46) and elevation (r = 0.43). An empirical linear relationship is presented as a combination of individually estimated $v_s30$ with weighting factors of 0.45, 0.45, and 0.1 for topographic slope, elevation, and mapped lithology, respectively. Due to a weak correlation between $v_s30$ obtained from inversion of dispersion curves and the proxy-based estimation (r = 0.50), however, the relatively large error range should be considered for applications of this relationship.