Woohyun Son

Frequency-domain waveform inversion using an l1-norm objective function

In general, seismic waveform inversion adopts an objective function based on the l2-norm. However, waveform inversion using the l2-norm produces distorted results because the l2-norm is sensitive to statistically invalid data such as outliers. As an alternative, there have been several studies applying l1-norm-based objective functions to waveform inversion. Although waveform inversion based on the l1-norm is known to produce robust inversion results against specific outliers in the time domain, its effectiveness and characteristics are yet to be studied in the frequency domain. The present study proposes an algorithm for l1-norm-based waveform inversion in the frequency domain. The proposed algorithm employs a structure identical to those used in conventional frequency-domain waveform inversion algorithms that exploit the back-propagation technique, but displays robustness against outliers, which has been confirmed based on inversion of the synthetic Marmousi model. The characteristics and advantages of the l1-norm were analysed by comparing it with the l2-norm. In addition, inversion was performed on data containing outliers to examine the robustness against outliers. The effectiveness of removing outliers was verified by using the l1-norm to calculate the residual wavefield and its spectrum for the data containing outliers.

Seismic reflection imaging of Quaternary faulting offshore the southeastern Korean Peninsula

The Yangsan Fault System (YFS) is a dominating tectonic structure in the southeastern part of the Korean Peninsula. The YFS consists of NNE-striking dextral strike-slip faults that are traced to the southeastern coast of the Korean Peninsula. We acquired high-resolution seismic profiles offshore the southeastern Korean Peninsula to investigate how the YFS extends offshore and constrain the age of fault activity using stratigraphic interpretation. The seismic profiles image near-vertical faults trending NE to NNE that constitute a fault zone similar to a duplex structure at a releasing bend of a right-lateral strike-slip fault. The faults are interpreted as an offshore extension of the Ilgwang fault that is a member of the YFS. Stratigraphic interpretation of seismic profiles indicates that the offshore faults were activated repeatedly in the Pliocene and Quaternary. The right-lateral activity of the Ilgwang fault is consistent with the current stress regime in and around the southeastern Korean Peninsula that dictates the P-axis direction in the E-W or ENE-WSW since the Pliocene.

Swell Effect Correction of Sub-bottom Profiler Data with Weak Sea Bottom Signal

A 3.5 kHz or chirp sub-bottom profiling survey is widely used in the marine geological and engineering purpose exploration. However, swells in the sea degrade the quality of the survey data. The horizontal continuity of profiler data can be enhanced and the quality can be improved by correcting the influence of the swell. Accurate detection of sea bottom location is important in correcting the swell effect. In this study, we tried to pick sea bottom locations by finding the position of crossing a threshold of the maximum value for the raw data and transformed data of envelope or energy ratio. However, in case of the low-quality data where the sea bottom signals are not clear due to sea wave noise, automatic sea bottom detection at the individual traces was not successful. We corrected the mispicks for the low quality data and obtained satisfactory results by picking a sea bottom within a range considering the previous average of sea bottom, and excluding unreliable big-difference picks. In case of trace by trace picking, fewest mispicks were found when using energy ratio data. In case of picking considering the previous average, the correction result was relatively satisfactory when using raw data.

A Study on Optimization of the Global-Correlation-Based Objective Function for the Simultaneous-Source Full Waveform Inversion with Streamer-Type Data

요약: 동시 송신원 전파형 역산 기법은 계산량을 획기적으로 줄여 전파형 역산의 적용성을 높여준다. 그러나 다수의 송신원 모음 자료를 동시에 모델링하여 사용하기 때문에 관측 자료의 수진기 위치가 송신원에 따라 다른 경우, 나머지(residual) 파동장에 불필요한 값을 생성하게 되고 이는 파형역산의 수렴성을 저해하게 된다. 특히, 제한된 벌림 거리(offset)를 갖는 스트리머 방식의 탐사자료는 동시 송신원 기법을 적용하기에 가장 어려운 자료 형태이다. 이러한 문제점을 극복하기 위해 최근에 global correlation에 기반한 목적함수가 제안되었고, 시간영역 전파형 역산에 성공적으로 적용되었다.그러나 이 기법은 변형된 목적함수를 사용하기 때문에 나머지 파동장이 왜곡되고 경우에 따라 역산 결과에 부정적인 영향을 주기도 한다. 또한, 여러 가지 장점을 갖고 있는 주파수 영역 파형역산에 적용된 사례는 아직 보고된 적이 없다. 본논문에서는 이러한 나머지 파동장의 왜곡을 최소화하기 위해 global correlation 계산 시 사용하는 자료에 진폭감쇠 기법을 적용한다. 진폭감쇠를 적용한 자료는 global correlation의 특성을 최적화하여 나머지 파동장의 왜곡을 줄이고 파형역산 결과를 향상시킨다. 시간 영역에서 구한 나머지 파동장을 주파수 영역에서 역전파시킴으로써 global correlation기법을주파수 영역에서 구현한다. 스트리머 방식의 합성 탐사자료를 이용한 예제를 통해 본 논문에서 제안한 기법이 기존의global correlation 목적함수에 기반한 동시 송신원 전파형 역산보다 향상된 결과를 얻을 수 있음을 보여준다. 주요어: 전파형 역산, 동시 송신원, 주파수 영역, 스트리머 탐사 자료, global correlationAbstract: The simultaneous-source full waveform inversion improves the applicability of full waveform inversion byreducing the computational cost. Since this technique adopts simultaneous multi-source for forward modeling, unwantedevents remain in the residual seismograms when the receiver geometry of field acquisition is different from that ofnumerical modeling. As a result, these events impede the convergence of the full waveform inversion. In particular, thestreamer-type data with limited offsets is the most difficult data to apply the simultaneous-source technique. To overcomethis problem, the global-correlation-based objective function was suggested and it was successfully applied to thesimultaneous-source full waveform inversion in time domain. However, this method distorts residual wavefields due tothe modified objective function and has a negative influence on the inversion result. In addition, this method has notbeen applied to the frequency-domain simultaneous-source full waveform inversion. In this paper, we apply a time-damping function to the observed and modeled data, which are used to compute global correlation, to minimize thedistortion of residual wavefields. Since the damped wavefields optimize the performance of the global correlation, itmitigates the distortion of the residual wavefields and improves the inversion result. Our algorithm incorporates the global-correlation-based full waveform inversion into the frequency domain by back-propagating the time-domain residualwavefields in the frequency domain. Through the numerical examples using the streamer-type data, we show that ourinversion algorithm better describes the velocity structure than the conventional global correlation approach does.Keywords: full waveform inversion, simultaneous-source, frequency-domain, streamer data,2012년 6월 19일 접수; 2012년 7월 4일 수정; 2012년 7월 13일 채택; global correlation*Corresponding authorE-mail: pyunsj@inha.ac.krAddress: Department of Energy Resources Engineering, Inha University, 253 Yonghyun-dong Nam-gu, Incheon 402-751, Korea

3D Laplace-domain Modeling, Including Configuration of the Sea Bottom Using the Gaussian Quadrature Method of Integration

3D Laplace-domain waveform inversion can recover a large velocity model for successive waveform inversion in the frequency domain. However, the grid interval in 3D Laplace-domain modeling and inversion cannot be sufficiently small because of the heavy computational cost. Therefore, we cannot assess whether or not the modeled wavefield is reliable if our model has an abruptly undulated sea bottom surface. The irregular finite element method can provide a solution; however, it increases the number of bands of the impedance matrix. Instead, we applied the Gaussian quadrature integration method in order to reflect two properties on one element at the irregular sea bottom. In order to verify this modeling algorithm, we compared our modeled wavefield with the analytic solutions for an unbounded homogeneous model, an unbounded two-layer model and an obliquely-inclined two-layer model. The results of the verification tests show that our modeling algorithm better describes a wavefield with an irregular sea bottom in the 3D Laplace domain than the conventional modeling algorithm.