• Geophysics and Geophysical Exploration
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• v.22 no.4
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• pp.195-201
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• 2019

The logarithmic objective function used in waveform inversion minimizes the logarithmic differences between the observed and modeled data. Laplace-domain waveform inversions usually adopt the logarithmic objective function and the diagonal elements of the pseudo-Hessian for optimization. In this case, we apply the Levenberg-Marquardt algorithm to prevent the diagonal elements of the pseudo-Hessian from being zero or near-zero values. In this study, we analyzed the diagonal elements of the pseudo-Hessian of the logarithmic objective function and showed that there is no zero or near-zero value in the diagonal elements of the pseudo-Hessian for acoustic waveform inversion in the Laplace domain. Accordingly, we do not need to apply the Levenberg-Marquardt algorithm when we regularize the gradient direction using the pseudo-Hessian of the logarithmic objective function. Numerical examples using synthetic and field datasets demonstrate that we can obtain inversion results without applying the Levenberg-Marquardt method.

• 한국지구물리탐사학회:학술대회논문집
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• 2007.06a
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• pp.130-134
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• 2007

Classical full waveform inversion for velocity estimation defines the objective function as the $l^2$ -norm of differences between the modeled and the observed wavefields. Although widely used, the results of this method have been less than satisfactory. A moderate improvement of this method is to define the objective function as the $l^2$ -norm of differences between the logarithms of the modeled and observed wavefields. In this paper we propose new objective functions of waveform inversion. They produce better results in sub-salt imaging than those of the classical and the logarithmic objective functions. One objective function defines the residual as the difference between $L^{th}$ power of the modeled wavefields and that of the observed wavefields. Another defines the residual as the difference between the integral of the $L^{th}$ power of the modeled wavefields and that of the observed wavefields. We apply these new objective functions to the synthetic SEG/EAGE salt model, and show that our new waveform inversion algorithms provide more accurate results than those of the classical and logarithmic waveform inversion methods.

• 한국지구물리탐사학회:학술대회논문집
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• 2007.06a
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• pp.118-123
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• 2007

A robust objective function in the frequency domain is applied to the acoustic full waveform inversion. The proposed objective function is defined as $l_1$-norm of residual wavefields in the frequency domain. Generally, the full waveform inversion is extremely sensitive to a number of factors such as parameterization, initial model, noise and so on. The numerical tests were performed for checking the sensitivity to attenuation and several noises. For the comparison with other objective functions, the conventional least-squares method and the logarithmic method were tested under the same condition. The synthetic data examples show that the proposed algorithm is more robust than the well-known methods.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1996.10a
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• pp.313-318
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• 1996

In this paper, a parametric study of the unbalance response and the stability is carried out to show the influence of seal parameters on the response of rotor. The seal parameters optimized are the seal clearance and the seal length. The minimum quantity of a Q factor in the critical speed and the maximum quantity of a logarithmic decreement in the operating speed, avoiding the reign of resonance, are the objective function. This paper describes a new approach to find a seal parameter of rotor system. The optimization method is used genetic algorithms, which are search algorithms based on the mechanics of natural selection and natural genetics. The results show the capability of this method and indicate that an optimal design of seals can improve the unbalance and the stability of rotor.

• Journal of Korea Water Resources Association
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• v.32 no.6
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• pp.711-720
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• 1999

In this study, a various rainfall-runoff modelling approaches have been applied to the runoff response of flood hydrograph in three experimental watershed of the western part of korea. Mathematical models of runoff response also have been studied including linear system theory based on modeling techniques. Eight models were operated at the five water level gauging stations and the parameters of each model were computed by the Rosenbrock's hill climbing method to minimize the objective function. For the parameter verification of the models, a different complex rainfall-runoff event was selected in the same of the three river basins and derived IUH of the each model could be calibrated. Furthermore multiple regressions of the logarithmic transformation method between model parameters and catchment characteristics were studied in the selected five station.

• Maxillofacial Plastic and Reconstructive Surgery
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• v.35 no.3
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• pp.167-173
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• 2013

Purpose: The aim of this study is to analyze the series of panoramic radiograph of implant patients using the system to measure peri-implant crestal bone loss according to the elapsed time from fixture installation time to more than three years. Methods: Choose 10 patients having 45 implant fixtures installed, which have series of panoramic radiograph in the period to be analyzed by the system. Then, calculated the crestal bone depth and statistics and selected the implant in concerned by clicking the implant of image shown on the monitor by the implemented pattern recognition system. Then, the system recognized the x, y coordination of the implant and peri-implant alveolar crest, and calculated the distance between the approximated line of implant fixture and alveolar crest. By applying pattern recognition to periodic panoramic radiographs, we attained the results and made a comparison with the results of preceded articles concerning peri-implant marginal bone loss. Analyzing peri-implant crestal bone loss in a regression analysis periodic filmed panoramic radiograph, logarithmic approximation had highest $R^2$ value, and the equation is as shown below. $y=0.245Logx{\pm}0.42$, $R^2=0.53$, unit: month (x), mm (y) Results: Panoramic radiograph is a more wide-scoped view compared with the periapical radiograph in the same resolution. Therefore, there was not enough information in the radiograph in local area. Anterior portion of many radiographs was out of the focal trough and blurred precluding the accurate recognition by the system, and many implants were overlapped with the adjacent structures, in which the alveolar crest was impossible to find. Conclusion: Considering the earlier objective and error, we expect better results from an analysis of periapical radiograph than panoramic radiograph. Implementing additional function, we expect high extensibility of pattern recognition system as a diagnostic tool to evaluate implant-bone integration, calculate length from fixture to inferior alveolar nerve, and from fixture to base of the maxillary sinus.