• Geophysics and Geophysical Exploration
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• v.15 no.3
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• pp.129-135
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• 2012

The simultaneous-source full waveform inversion improves the applicability of full waveform inversion by reducing the computational cost. Since this technique adopts simultaneous multi-source for forward modeling, unwanted events remain in the residual seismograms when the receiver geometry of field acquisition is different from that of numerical modeling. As a result, these events impede the convergence of the full waveform inversion. In particular, the streamer-type data with limited offsets is the most difficult data to apply the simultaneous-source technique. To overcome this problem, the global-correlation-based objective function was suggested and it was successfully applied to the simultaneous-source full waveform inversion in time domain. However, this method distorts residual wavefields due to the modified objective function and has a negative influence on the inversion result. In addition, this method has not been applied to the frequency-domain simultaneous-source full waveform inversion. In this paper, we apply a timedamping function to the observed and modeled data, which are used to compute global correlation, to minimize the distortion of residual wavefields. Since the damped wavefields optimize the performance of the global correlation, it mitigates the distortion of the residual wavefields and improves the inversion result. Our algorithm incorporates the globalcorrelation-based full waveform inversion into the frequency domain by back-propagating the time-domain residual wavefields in the frequency domain. Through the numerical examples using the streamer-type data, we show that our inversion algorithm better describes the velocity structure than the conventional global correlation approach does.

• 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.

• 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.

• 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.

• Journal of the Earthquake Engineering Society of Korea
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• v.13 no.5
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• pp.23-29
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• 2009

On December 13, 1996, an earthquake with local magnitude (M$_L$) 4.5 occurred in the Yeongwol area of South Korea. The epicenter was 37.2545$^{\circ}$N and 128.7277$^{\circ}$E, which is located inside the Okcheon Fold Belt. The waveform inversion analysis was carried out to estimate source parameters of the event according to the filtering bandwidth of seismic data. Using 0.02$\sim$0.2 Hz filtering bandwidth, focal depth and seismic moment were estimated to be 6 km and 1.3$\times$10$^{16}$ N$\cdot$m, respectively. This seismic moment corresponds to the moment magnitude (M$_W$) 4.7. The focal mechanism by the waveform inversion and P wave first motion polarity analysis is a strike slip faulting including a small thrust component, and the direction of P-axis is ENE-WSW. The moment magnitude estimated by spectral analysis was 4.8, which is similar to that estimated by waveform inversion. Average stress drop was estimated to be 14.3 MPa.

• 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.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.34 no.4
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• pp.221-230
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• 2021

This paper proposes full waveform inversion (FWI) for estimating the physical properties of a layered half-space. An FWI solution is obtained using a genetic algorithm (GA), which is a well-known global optimization approach. The dynamic responses of a layered half-space subjected to a harmonic vertical disk load are measured and compared with those calculated using the estimated physical properties. The responses are calculated using the thin-layer method, which is accurate and efficient for layered media. Subsequently, a numerical model is constructed for a layered half-space using mid-point integrated finite elements and perfectly matched discrete layers. An objective function of the global optimization problem is defined as the L2-norm of the difference between the observed and estimated responses. A GA is used to minimize the objective function and obtain a solution for the FWI. The accuracy of the proposed approach is applied to various problems involving layered half-spaces. The results verify that the proposed FWI based on a GA is suitable for estimating the material properties of a layered half-space, even when the measured responses include measurement noise.

• Geophysics and Geophysical Exploration
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• v.17 no.4
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• pp.231-241
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• 2014

Recently, single channel seismic survey for engineering purpose have been used widely taking advantage of simple processing. However it is very difficult to obtain high fidelity subsurface image by single channel seismic due to insufficient fold coverage. Recently, seismic waveform inversion in multi channel seismic survey is utilized for accurate subsurface imaging even in complex terrains. In this paper, we propose the seismic waveform inversion algorithm for velocity model building using a single channel seismic data. We utilize the Gauss-Newton method and assume that subsurface model is 1-Dimensional. Seismic source estimation technique is used and offset effect is also corrected by removing delay time by offset. Proposed algorithm is verified by applying modified Marmousi2 model, and applied to field data set obtained in port of Busan.

• Geophysics and Geophysical Exploration
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• v.17 no.4
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• pp.187-201
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• 2014

Compared with the separated inversion of electromagnetic (EM) and seismic data, a joint inversion using both EM and seismic data reduces the uncertainty and gives the opportunity to use the advantage of each data. Seismic fullwaveform inversion allows velocity information with high resolution in complicated subsurface. However, it is an indirect survey which finds the structure containing oil and gas. On the other hand, marine controlled-source EM (mCSEM) inversion can directly indicate the oil and gas using different EM properties of hydrocarbon with marine sediments and cap rocks whereas it has poor resolution than seismic method. In this paper, we have developed a joint EM inversion algorithm using a cross-gradient technique. P-wave velocity structure obtained by full-waveform inversion using plane wave encoding is used as structure constraints to calculate the cross-gradient term in the joint inversion. When the jointinversion algorithm is applied to the synthetic data which are simulated for subsea reservoir exploration, images have been significantly improved over those obtained from separate EM inversion. The results indicate that the developed joint inversion scheme can be applied for detecting reservoir and calculating the accurate oil and gas reserves.

• Geophysics and Geophysical Exploration
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• v.12 no.1
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• pp.99-104
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• 2009

We propose a waveform inversion method for SH-wave data obtained in a shallow seismic refraction survey, to determine a 2D inhomogeneous S-wave profile of shallow soils. In this method, a 2.5D equation is used to simulate SH-wave propagation in 2D media. The equation is solved with the staggered grid finite-difference approximation to the 4th-order in space and 2nd-order in time, to compute a synthetic wave. The misfit, defined using differences between calculated and observed waveforms, is minimised with a hybrid heuristic search method. We parameterise a 2D subsurface structural model with blocks with different depth boundaries, and S-wave velocities in each block. Numerical experiments were conducted using synthetic SH-wave data with white noise for a model having a blind layer and irregular interfaces. We could reconstruct a structure including a blind layer with reasonable computation time from surface seismic refraction data.