GEOLOGICALLY CONSTRAINED FULL WAVEFORM INVERSION

Sukjoon PYUN,Yunhui PARK 한국산업응용수학회 2013 한국산업응용수학회 학술대회 논문집 Vol.8 No.1

It is apparent that full waveform inversion with regularization shows a better result than with no regularization. However, it may fail to delineate sharp geological structures such as faults and salt boundaries. Hence, the geological information should be considered to recover accurate subsurface structures. In this paper, an adaptive smoothing regularization is implemented based on local slope. The adaptive regularization incorporates geological information into inversion process. Local slopes are calculated using the Hilbert transform and stabilized through isotropic and edge-enhancing smoothing before and after calculating local slopes, respectively. The adaptive smoothing regularization is applied to the full waveform inversion for a synthetic subsurface model. The inversion result shows that the layer interfaces are faithfully preserved and sharpened.

Comparison of waveform inversion, part 3: amplitude approach

Pyun, Sukjoon,Shin, Changsoo,Bednar, J. B. unknown 2007 Geophysical prospecting Vol.55 No.4

<P>ABSTRACT</P><P>In the second paper of this three part series, we studied the case of conventional and logarithmic phase-only approaches to full-waveform inversion. Here, we concentrate on deriving amplitude-only approaches for both conventional- and logarithmic-based methods. We define two amplitude-only objective functions by simply assuming that the phase of the modelled wavefield is equal to that of the observed wavefield. We do this for both the conventional least-squares approach and the logarithmic approach of Shin and Min. We show that these functions can be optimized using the same reverse-time propagation algorithm of the full conventional methodology. Although the residuals in this case are not really residual wavefields, they can both be considered and utilized in that sense. In contrast to the case for our phase-only algorithms, we show through numerical tests that the conventional amplitude-only inversion is better than the logarithmic method.</P>

SIMULTANEOUS-SOURCE FULL WAVEFORM INVERSION AND ITS COMPUTATIONAL EFFICIENCY

Sukjoon PYUN 한국산업응용수학회 2013 한국산업응용수학회 학술대회 논문집 Vol.8 No.1

Refraction traveltime tomography using damped monochromatic wavefield

Sukjoon Pyun,Changsoo Shin 한국암반공학회 2003 한국암반공학회 학술대회 및 세미나 자료집 Vol.- No.-

Stretch가 없는 수직 시간차 보정

편석준 ( Sukjoon Pyun ) 한국지구물리·물리탐사학회 2017 지구물리와 물리탐사 Vol.20 No.4

NMO보정은 탄성파 반사법 자료처리의 핵심적인 과정이고, AVO분석을 위해 가장 중요한 자료처리 단계이다. 그러나 NMO보정이 갖고 있는 근본적인 문제인 stretch 현상은 겹쌓기 단면의 품질을 저해하고 AVO분석의 신뢰성을 떨어뜨린다. 이 문제점을 해결하기 위해서 일반적으로 뮤팅을 수행하지만 stretch가 없는 NMO보정 기술을 적용한다면 먼 거리 벌림 자료의 활용도가 높아진다. 이 논문에서는 먼저 NMO보정의 개념과 방법, 그리고 stretch 현상의 원인 및 특성에 대해 설명한다. Stretch 현상에 대한 직관적인 이해를 위해 단순화된 모형반응에 대한 NMO보정을 보여주고, 정량적인 이해를 위해 NMO보정에 대한 이론 식을 설명한다. Stretch를 제거하는 뮤팅에 대해 설명함으로써 기존 방법의 한 계점과 새로운 해결책에 대한 필요성에 대해 논한다. Stretch가 없는 NMO보정 기법은 여러 가지 종류가 있는데 여기서는 역산 이론에 의해 이를 구현하는 방법을 사용하였다. 마지막으로 역산 기법을 통해 구현한 stretch가 없는 NMO보정을 합성자료와 현장자료에 적용하여 실제 성능을 확인해 보았다. 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.

파동방정식 수치해의 일관성에 관한 연구

편석준 ( Sukjoon Pyun ),박윤희 ( Yunhui Park ) 한국지구물리·물리탐사학회 2016 지구물리와 물리탐사 Vol.19 No.3

탄성파 자료의 역산은 파동방정식에 기초하고 있으므로 파동방정식의 해를 정확하게 구하는 것이 가장 중요하다. 특히, 전파형역산은 파동장 전체를 이용하기 때문에 정문제에 해당하는 모델링이 정확하게 이루어져야 신뢰할 수 있는 결과를 얻게 된다. 파동방정식의 수치해를 구하는 대표적인 기법인 유한차분법과 유한요소법은 해의 수렴성을 보장할 수 있어야 하는데, 해의 수렴성은 이론적으로 일반화된 증명이 되어 있으나 실제 문제에 적용할 경우 일관성과 안정성을 분석해야 한다. 모델링 결과의 일관성은 송신원 함수의 구현이 매우 중요한 부분인데, 유한차분법은 디랙 델타 함수(Dirac delta function)를 나타낼 때 격자 간격으로 표준화된 싱크 함수(sinc function)를 사용해야 하는 반면 유한요소법은 격자 간격에 관계없이 기저함수 값을 사용하면 된다. 주파수 영역 파동방정식을 사용할 경우 송신 파형 함수의 스펙트럼을 정확하게 표현하기 위해 샘플링 이론으로 정의되는 시간 간격보다 더 조밀한 샘플링 간격을 사용하고 나이퀴스트(Nyquist) 주파수보다 더 높은 주파수를 최대 주파수로 사용해야 한다. 또한, 복소 각주파수를 사용하는 경우 감쇠 파동방정식을 만족하기 위해서는 송신 파형 함수를 먼저 감쇠한 후 사용해야 한다. 이러한 요건들이 모두 만족되었을 때 신뢰할 수 있는 역산 알고리즘 개발이 가능하다. 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.

Source wavelet estimation using common mid-point gathers

Park, Yunhui,Pyun, Sukjoon Informa UK (Taylor Francis) 2015 Geosystem engineering Vol.18 No.4

Refraction traveltime tomography based on damped wave equation for irregular topographic model

Park, Yunhui,Pyun, Sukjoon Elsevier 2018 Journal of applied geophysics Vol.150 No.-

<P><B>Abstract</B></P> <P>Land seismic data generally have time-static issues due to irregular topography and weathered layers at shallow depths. Unless the time static is handled appropriately, interpretation of the subsurface structures can be easily distorted. Therefore, static corrections are commonly applied to land seismic data. The near-surface velocity, which is required for static corrections, can be inferred from first-arrival traveltime tomography, which must consider the irregular topography, as the land seismic data are generally obtained in irregular topography.</P> <P>This paper proposes a refraction traveltime tomography technique that is applicable to an irregular topographic model. This technique uses unstructured meshes to express an irregular topography, and traveltimes calculated from the frequency-domain damped wavefields using the finite element method. The diagonal elements of the approximate Hessian matrix were adopted for preconditioning, and the principle of reciprocity was introduced to efficiently calculate the Fréchet derivative. We also included regularization to resolve the ill-posed inverse problem, and used the nonlinear conjugate gradient method to solve the inverse problem.</P> <P>As the damped wavefields were used, there were no issues associated with artificial reflections caused by unstructured meshes. In addition, the shadow zone problem could be circumvented because this method is based on the exact wave equation, which does not require a high-frequency assumption. Furthermore, the proposed method was both robust to an initial velocity model and efficient compared to full wavefield inversions. Through synthetic and field data examples, our method was shown to successfully reconstruct shallow velocity structures. To verify our method, static corrections were roughly applied to the field data using the estimated near-surface velocity. By comparing common shot gathers and stack sections with and without static corrections, we confirmed that the proposed tomography algorithm can be used to correct the statics of land seismic data.</P> <P><B>Highlights</B></P> <P> <UL> <LI> A refraction traveltime tomography is developed to invert near-surface velocity. </LI> <LI> The finite-element method using unstructured mesh is used to handle irregular topography. </LI> <LI> Traveltimes and Fréchet derivatives are calculated using frequency-domain damped wavefield. </LI> <LI> The proposed algorithm is proved to be applicable to real seismic data. </LI> </UL> </P>

An efficient wavenumber–space–time domain finite-difference modeling of acoustic wave equation for synthesizing CMP gathers

Park, Yunhui,Pyun, Sukjoon,Ha, Wansoo Informa UK (Taylor Francis) 2014 Geosystem engineering Vol.17 No.5

Implementation of adaptive edge-preserving smoothing regularisation technique for simultaneous multi-frequency full waveform inversion

Park, Yunhui,Pyun, Sukjoon Informa UK (Taylor Francis) 2015 EXPLORATION GEOPHYSICS -AUSTRALIA- Vol.46 No.2