• Journal of the Korean earth science society
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• v.37 no.5
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• pp.277-285
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• 2016

We introduce a depth scaling strategy to improve the accuracy of frequency-domain elastic full waveform inversion (FWI) using the new pseudo-Hessian matrix for seismic data without low-frequency components. The depth scaling strategy is based on the fact that the damping factor in the Levenberg-Marquardt method controls the energy concentration in the gradient. In other words, a large damping factor makes the Levenberg-Marquardt method similar to the steepest-descent method, by which shallow structures are mainly recovered. With a small damping factor, the Levenberg-Marquardt method becomes similar to the Gauss-Newton methods by which we can resolve deep structures as well as shallow structures. In our depth scaling strategy, a large damping factor is used in the early stage and then decreases automatically with the trend of error as the iteration goes on. With the depth scaling strategy, we can gradually move the parameter-searching region from shallow to deep parts. This flexible damping factor plays a role in retarding the model parameter update for shallow parts and mainly inverting deeper parts in the later stage of inversion. By doing so, we can improve deep parts in inversion results. The depth scaling strategy is applied to synthetic data without lowfrequency components for a modified version of the SEG/EAGE overthrust model. Numerical examples show that the flexible damping factor yields better results than the constant damping factor when reliable low-frequency components are missing.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.26 no.4
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• pp.223-231
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• 2013

This paper presents a time-domain Gauss-Newton full-waveform inversion method for the material profile reconstruction in heterogeneous semi-infinite solid media. To implement the inverse problem in a finite computational domain, perfectly-matchedlayers( PMLs) are introduced as wave-absorbing boundaries within which the domain's wave velocity profile is to be reconstructed. The inverse problem is formulated in a partial-differential-equations(PDE)-constrained optimization framework, where a least-squares misfit between measured and calculated surface responses is minimized under the constraint of PML-endowed wave equations. A Gauss-Newton-Krylov optimization algorithm is utilized to iteratively update the unknown wave velocity profile with the aid of a specialized regularization scheme. Through a series of one-dimensional examples, the solution of the Gauss-Newton inversion was close enough to the target profile, and showed superior convergence behavior with reduced wall-clock time of implementation compared to a conventional inversion using Fletcher-Reeves optimization algorithm.

• 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.1 no.1
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• pp.49-56
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• 1998

Seismic tomography has been widely used as high resolution subsurface imaging techniques in engineering applications. Although most of the techniques have been using travel time inversion, waveform method is being driven forward owing to the progress of computational environments. Although full-waveform inversion method has been known as the best method in terms of model resolving power without high-frequency restriction and weak scattering approximation, it has practical disadvantage that it is apt to get stuck in local minimum if the initial guess is far from the actual model and it consumes so much time to calculate. In this study, 2-D full-waveform inversion algorithm in acoustic medium is developed, which uses result of traveltime tomography as initial model. From the application on synthetic data, it is proved that this approach can efficiently reduce the problem of conventional approaches: our algorithm shows much faster convergence rate and improvement of model resolution. Result of application on physical modeling data also shows much improvement. It is expected that this algorithm can be applicable to real data.

• Geophysics and Geophysical Exploration
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• v.16 no.4
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• pp.211-216
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• 2013

In general, smoothing filters regularize functions by reducing differences between adjacent values. The smoothing filters, therefore, can regularize inverse solutions and produce more accurate subsurface structure when we apply it to full waveform inversion. If we apply a smoothing filter with a constant coefficient to subsurface image or velocity model, it will make layer interfaces and fault structures vague because it does not consider any information of geologic structures and variations of velocity. In this study, we develop a selective smoothing regularization technique, which adapts smoothing coefficients according to inversion iteration, to solve the weakness of smoothing regularization with a constant coefficient. First, we determine appropriate frequencies and analyze the corresponding wavenumber coverage. Then, we define effective maximum wavenumber as 99 percentile of wavenumber spectrum in order to choose smoothing coefficients which can effectively limit the wavenumber coverage. By adapting the chosen smoothing coefficients according to the iteration, we can implement multi-scale full waveform inversion while inverting multi-frequency components simultaneously. Through the successful inversion example on a salt model with high-contrast velocity structures, we can note that our method effectively regularizes the inverse solution. We also verify that our scheme is applicable to field data through the numerical example to the synthetic data containing random noise.

• Journal of the Earthquake Engineering Society of Korea
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• v.18 no.5
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• pp.213-219
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• 2014

The source parameters of four earthquakes with magnitude larger than 4.0 nearby the offshore Sinan are analyzed. The waveform inversion method is used for analyzing the source parameters of two events (20 August 2012 and 21 April 2013) with C&B and AK135-c crustal velocity structure models. The source parameters of the other two events (26 July 1994 and 23 March 2003) are obtained from references. Focal mechanisms of the events are strike slip faulting or strike slip faulting with a thrust component. The directions of P-axes of the events are ENE-WSW or NE-SW which are similar to previous studies on P-axes in and around the Korean peninsula. With regard to the events nearby the offshore Sinan, the regional stress, rather than being local stress, is seen to be the result of the combination of tectonic forces from the compression of plates colliding to the Eurasian Plate.

• Geophysics and Geophysical Exploration
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• v.7 no.1
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• pp.19-24
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• 2004

Frequency-space domain full-wave tomography is a promising technique for delineating detailed subsurface structure with high resolution. However, this method requires criteria for the selection of a set of optimal temporal frequency components, to achieve stability in the sequence of inversion processes together with computational efficiency. We propose a method of selecting optimal temporal frequencies, based on wavenumber continuity. The proposed method is tested numerically and is shown to be able to select an optimal set of frequency components that are sufficient to image the anomalies.

• 한국지구물리탐사학회:학술대회논문집
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• 2007.06a
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• pp.113-117
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• 2007

Sub-salt imaging is an unsolved hot issue in subsurface imaging area. We tested several important properties in imaging sub-salt structures to provide a clue to this problem. Reverse time migration using velocity models obtained by waveform inversion produced better results than that of stacking velocity analysis. Sub-salt imaging results were highly dependent on the size and shape of a salt structure. The results were not clear when the velocity of a salt structure is significantly higher than that of adjacent layers.

• Proceedings of the Korean Geotechical Society Conference
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• 1996.10a
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• pp.203-208
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• 1996

• The Journal of the Acoustical Society of Korea
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• v.34 no.6
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• pp.487-492
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• 2015

A short-range underwater target detection and identification techniques using mid- and high-frequency bands have been highly developed. However, nowadays the long-range detection using the low-frequency band is requested and one of the most challengeable issues. The waveform inversion technique is widely used and the hottest technology in both academia and industry of the seismic exploration. It is based on the numerical analysis tool, and could construct more than a few kilometers of the subsurface structures and model-parameters such as P-wave velocity using a low-frequency band. By applying this technique to the underwater acoustic circumstance, firstly application of underwater target detection is verified. Furthermore, subsurface structures and it's parameters of the war-field are well reconstructed. We can confirm that this technique greatly reduces the false-alarm rate for the underwater targets because it could accurately reproduce both the shape and the model-parameters at the same time.