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Robust Full Waveform Inversion Using Normalized Residual in the Frequency Domain
편석준 한국자원공학회 2011 Geosystem engineering Vol.14 No.1
A robust objective function for the full waveform inversion has been suggested in the frequency domain. The proposed objective function is defined as sum of complex absolute values of residual wavefields in the frequency domain. Generally, the full waveform inversion is extremely sensitive to the parameterization, frequency bandwidth, attenuation,noise and so on. Especially, noise is the most important factor in the full waveform inversion. In the frequency-domain waveform inversion, the attenuation of wavefields is one of the critical parameters for successful inversion. To verify the robustness of our algorithm, the proposed inversion scheme was tested in terms of the sensitivity to attenuation and noise. The comparison examples with both the conventional l2-norm and the logarithmic objective function demonstrated that the proposed inversion algorithm is robust to noise and less sensitive to attenuation.
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편석준,박윤희 한국지구물리.물리탐사학회 2022 지구물리와 물리탐사 Vol.25 No.4
Full waveform inversion (FWI) in the field of seismic data processing is an inversion technique that is used to estimate the velocity model of the subsurface for oil and gas exploration. Recently, deep learning (DL) technology has been increasingly used for seismic data processing, and its combination with FWI has attracted remarkable research efforts. For example, DL-based data processing techniques have been utilized for preprocessing input data for FWI, enabling the direct implementation of FWI through DL technology. DL-based FWI can be divided into the following methods: pure data-based, physics-based neural network, encoder–decoder, reparameterized FWI, and physics-informed neural network. In this review, we describe the theory and characteristics of the methods by systematizing them in the order of advancements. In the early days of DL-based FWI, the DL model predicted the velocity model by preparing a large training data set to adopt faithfully the basic principles of data science and apply a pure data-based prediction model. The current research trend is to supplement the shortcomings of the pure data-based approach using the loss function consisting of seismic data or physical information from the wave equation itself in deep neural networks. Based on these developments, DL-based FWI has evolved to not require a large amount of learning data, alleviating the cycle-skipping problem, which is an intrinsic limitation of FWI, and reducing computation times dramatically. The value of DL-based FWI is expected to increase continually in the processing of seismic data. 전파형 역산은 석유가스 탐사를 위한 탄성파 자료처리 분야에서 지층의 속도 모델을 추정하는데 사용되는 역산 기법이다. 최근 탄성파 자 료처리에 딥러닝 기술의 활용이 급격하게 증가하고 있는데, 전파형 역산 기술도 마찬가지로 다양한 연구가 이루어지고 있다. 초기에는 머 신러닝 기술을 활용한 자료처리 기법이 전파형 역산을 위한 입력자료의 전처리 목적으로 활용되는 수준이었으나, 딥러닝 기술을 통해 전 파형 역산을 직접적으로 구현하는 연구가 등장하기 시작하였다. 딥러닝 기술을 활용한 전파형 역산은 순수 데이터 기반 접근법, 물리 기 반 신경망 활용법, 인코더-디코더 구조 활용법, 신경망 재매개변수화를 이용한 구현법, 물리정보 기반 신경망 기법 등으로 구분할 수 있 다. 이 논문에서는 딥러닝 기반 전파형 역산 기법을 발전 과정 순서로 체계화하여 각각의 접근법에 대한 이론과 특징을 설명하였다. 전파 형 역산 기술에 딥러닝 기법을 도입한 초기에는 데이터 과학의 기본 원리에 충실하게 대량의 학습자료를 준비하고 순수 데이터 기반 예 측 모델을 적용하여 속도 모델을 역산하는 연구로 시작하였다. 최근 연구 동향은 탄성파 자료의 잔차나 파동방정식 자체의 물리정보를 심 층 신경망에 활용하여 순수 데이터 기반 접근법의 단점을 보완해 나가는 방향으로 진행되고 있다. 이러한 발전으로 대량의 학습자료가 필 요하지 않고, 전파형 역산의 태생적 한계점인 주기 놓침 현상을 완화하며 계산 시간을 획기적으로 줄일 수 있는 딥러닝 기반 전파형 역산 기술이 등장하고 있다. 딥러닝 기술의 도입으로 전파형 역산 기술은 탄성파 자료처리 분야에서 가치가 더 높아질 것으로 생각된다.
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편석준 ( Sukjoon Pyun ) 한국지구물리·물리탐사학회 2017 지구물리와 물리탐사 Vol.20 No.4
Normal moveout correction is one of the main procedures of seismic reflection data processing and a crucial pre-processing step for AVO analysis. Unfortunately, stretch phenomenon, which is the intrinsic problem of NMO correction, degrades the quality of stack section and reliability of AVO analysis. Although muting is applied to resolve this problem, it makes far-offset traces more useful to develop an advanced NMO correction technique without stretch. In this paper, easy and detailed explanations are provided on the definition and methodology of NMO correction, and then the cause of stretch is explained with its characteristics. A graphical explanation for NMO correction is given for the intuitive understanding of stretch phenomenon. Additionally, the theoretical formulation is derived to quantitatively understand the NMO correction. Through explaining the muting process to remove NMO stretch, the limitations of conventional methods are investigated and the need for a new resolution comes to discussion. We describe a stretchfree NMO correction based on inverse theory among many different stretch-free NMO corrections. Finally, the stretchfree NMO correction is verified through synthetic example and real data.
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편석준 ( Sukjoon Pyun ),박윤희 ( Yunhui Park ) 한국지구물리·물리탐사학회 2016 지구물리와 물리탐사 Vol.19 No.3
Since seismic inversion is based on the wave equation, it is important to calculate the solution of wave equation exactly. In particular, full waveform inversion would produce reliable results only when the forward modeling is accurately performed because it uses full waveform. When we use finite-difference or finite-element method to solve the wave equation, the convergence of numerical scheme should be guaranteed. Although the general proof of convergence is provided theoretically, the consistency and stability of numerical schemes should be verified for practical applications. The implementation of source function is the most crucial factor for the consistency of modeling schemes. While we have to use the sinc function normalized by grid spacing to correctly describe the Dirac delta function in the finite-difference method, we can simply use the value of basis function, regardless of grid spacing, to implement the Dirac delta function in the finite-element method. If we use frequency-domain wave equation, we need to use a conservative criterion to determine both sampling interval and maximum frequency for the source wavelet generation. In addition, the source wavelet should be attenuated before applying it for modeling in order to make it obey damped wave equation in case of using complex angular frequency. With these conditions satisfied, we can develop reliable inversion algorithms.
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