• 한국지구물리탐사학회:학술대회논문집
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• 2006.06a
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• pp.131-135
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• 2006

A seismic waveform inversion for prestack seismic data based on the Gauss-Newton method is presented. The Gauss-Newton method for seismic waveform inversion was proposed in the 80s but has rarely been studied. Extensive computational and memory requirements have been principal difficulties. To overcome this, we used different sizes of grids in the inversion stage from those of grids in the wave propagation simulation, temporal windowing of the simulation and approximation of virtual sources for calculating partial derivatives, and implemented this algorithm on parallel supercomputers. We show that the Gauss-Newton method has high resolving power and convergence rate, and demonstrate potential applications to real seismic data.

• Communications of the Korean Mathematical Society
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• v.16 no.3
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• pp.445-458
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• 2001

The shape and the distribution of material construction of the scatterer may be obtained from its scattered fields by the iterative inversion in the spectral domain. The illposedness, the resolution, and the uniqueness of the inversion are the key problems in the inversion and inter-related. The illposedness is shown to be caused by the evanescent modes which carries and amplifies exponentially the measurement errors in the back-propagation of the measured scattered fields. By filtering out all the evanescent modes in the cost functional defined as the squared difference between the measured and the calculated spatial spectrum of the scattered fields from the iteratively chosen medium parameters of the scatterer, one may regularize the illposedness of the inversion in the expense of the resolution. There exist many local minima of the cost functional for the inversion of the large and the high-contrast scatterer and the hybrid algorithm combining the genetic algorithm and the Levenberg-Marquardt algorithm is shown to find efficiently its global minimum. The resolution of reconstruction obtained by keeping all the propating modes and filtering out the evanescent modes for the regularization becomes 0.5 wavelength. The super resolution may be obtained by keeping the evanescent modes when the measurement error and instance, respectively, are small and near.

• Bulletin of the Korean Mathematical Society
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• v.35 no.2
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• pp.345-362
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• 1998

We introduce and anlyze a naturally parallelizable frequency-domain method for parabolic problems with a Neumann boundary condition. After taking the Fourier transformation of given equations in the space-time domain into the space-frequency domain, we solve an indefinite, complex elliptic problem for each frequency. Fourier inversion will then recover the solution of the original problem in the space-time domain. Existence and uniqueness of a solution of the transformed problem corresponding to each frequency is established. Fourier invertibility of the solution in the frequency-domain is also examined. Error estimates for a finite element approximation to solutions fo transformed problems and full error estimates for solving the given problem using a discrete Fourier inverse transform are given.

• Tunnel and Underground Space
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• v.15 no.5 s.58
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• pp.352-358
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• 2005

For non-destructive testing of concrete structures, time and frequency domain method were applied to detect cavity in underground model and pier model. To interpret the measured data, time domain method made use of tomography which was completed with first arrivaltime and inversion method. In this steady, frequency domain method using Fourier transform was tried. Maximum frequency in the frequency domain was analyzed to calculate location of cavity.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.15 no.3
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• pp.124-127
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• 2005

It is demonstrated that the annealing process for Ti in-diffusion to z-cut $LiNbO_3$ at temperature lower than the curie temperature in a platinum (Pt) box can cause a ferroelectric micro-domain inversion at the +z surface and Li out-diffusion, therefore which should be avoided or suppressed for waveguide type periodically poled lithium niobate (PPLN) devices. The depth of the inversion layer depends on the Ti-diffusion conditions such as temperature, atmosphere, the sealing method of $LiNbO_3$ in the Pt box and crystal orientation is experimentally examined. The result shows that the polarization-inverted domain boundary appears at the only +z surface and its thickness is about $1.6{\mu}m$. Also, for the etched $LiNbO_3$, surface the domain shape was observed by the optical microscope and atomic force microscopy (AEM), and distribution of the cation concentrations in the $LiNbO_3$ crystal by the secondary ion mass spectrometry (SIMS).

• Journal of the Korean Institute of Telematics and Electronics A
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• v.31A no.5
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• pp.39-49
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• 1994

In this paper, An inversion technique to reconstruct permittivity profiles of 2-D inhomogeneous dielectric objects by iterativeprocess using the moment-methodand improved newton's algoritham is presented. In order to reduce the noise effect in the scattered fieldon the reconstructed permittivity profiles, the cell size of inversescattering is made be larger than that of forward scattering. Performing numerical calculations of dielectric scatterer it is demonstrated that this inversion is able to reconstruct dielectric objectshaving large size and inhomogeneous characteristics, which is insentive tothe noise effect in the scattered field on the reconstructed result.

• 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.

• 한국지구물리탐사학회:학술대회논문집
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• 2006.06a
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• pp.3-6
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• 2006

There are three types of frequency-domain loop-loop EM induction method, depending on the loop separation and their location relative to the ground surface: horizontal-loop EM (HLEM), fixed small-loop EM, and helicopter-borne EM (HEM) methods. Multidimensional inversion provides tomographic images of the subsurface resistivity structure and thus enhances the interpretational accuracy of loop-loop EM data. HLEM method is shown to be effective for exploring groundwater resources in weathered and fractured crystalline basement terrains in semi-arid regions. Also, HEM method is useful for locating weak zones in landslide areas. The applicability of inversion to small-loop EM data depends solely on the S/N ratio. The quadrature response of small-loop EM data can only give the equivalent conductivity of a homogenous half-space model, and thus the in-phase component is essential in inverting EM data. However, the in-phase response is much lower and decreases more rapidly with decreasing frequency than the quadrature response. Further work is needed to obtain conductivity-depth images from small-loop EM data.

• Proceedings of the Earthquake Engineering Society of Korea Conference
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• 2003.03a
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• pp.45-49
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• 2003

The velocity structure beneath the CHNB broadband station is determined by receiver function analysis using by from teleseismic P waveforms. The detailed broadband receiver functions are obtained by stacking method for source-equalized vertical, radial and tangential components of teleseismic P waveforms. A time domain inversion uses the stacked radial receiver function to determine vertical P wave velocity structure beneath the station. The crustal velocity structures beneath the stations are estimated using the receiver function inversion method in the case at the crustal model parameterized by many thin, flat-tying, homogeneous layers. The result of crust at model inversion shows the crustal velocity structure beneath the CHNB station varies smoothly with increasing depth, and there are six discontinuity around 2.5km, 6.25km, 12.5km, 22.5km and 27.5km depth, with Moho discontinuity at about 32.5km depth.

• Proceedings of the Earthquake Engineering Society of Korea Conference
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• 2003.09a
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• pp.3-7
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• 2003

The velocity structure beneath the CHNB broadband station is determined by receiver function analysis using by from teleseismic P waveforms. The detailed broadband receiver functions are obtained by stacking method for source-equalized vertical, radial and tangential components of teleseismic P waveforms. A time domain inversion uses the stacked radial receiver function to determine vertical P wave velocity structure beneath the station. The crustal velocity structures beneath the stations are estimated using the receiver function inversion method in the case at the crustal model parameterized by many thin, flat-lying, homogeneous layers. Events divide into 4 groups. four azimuths corresponding to events in group a(southwest), b(south), c(southeast), d(northeast). The result of crust at model inversion shows the crustal velocity structure beneath the CHNB station varies smoothly with increasing depth. The conard discontinuity lies around 18 km and moho discontinuity lies range from 30 to 34 km.