Geophysics and Geophysical Exploration (지구물리와물리탐사)

Korean Society of Earth and Exploration Geophysicists (한국지구물리·물리탐사학회)
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Full Waveform Inversion using a Cyclic-shot Subsampling and a Reference-shot Subset

주기적 송신원 추출과 참조 송신원 부분집합을 이용한 완전 파형 역산

  • Jo, Sang Hoon (Trinity Engineering) ;
  • Ha, Wansoo (Department of Energy Resources Engineering, Pukyong National University)
  • 조상훈 (트리니티 엔지니어링) ;
  • 하완수 (부경대학교 에너지자원공학과)
  • Received : 2019.01.31
  • Accepted : 2019.05.06
  • Published : 2019.05.31
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Abstract

In this study, we presented a reference-shot subset method for stable convergence of full waveform inversion using a cyclic-shot subsampling technique. Full waveform inversion needs repetitive modeling of wave propagation and thus its calculation time increases as the number of sources increases. In order to reduce the computation time, we can use a cyclic-shot subsampling method; however, it makes the cost function oscillate in the early stage of the inversion and causes a problem in applying the convergence criteria. We introduced a method in which the cost function is calculated using a fixed reference-shot subset while updating the model parameters using the cyclic-shot subsampling method. Through the examples of full waveform inversion using the Marmousi velocity model, we confirmed that the convergence of cost function becomes stable even under the cyclic-shot subsampling method if using a reference-shot subset.

본 연구에서는 주기적 송신원 추출 기법을 사용한 완전 파형 역산 시 목적함수의 안정적인 수렴을 위해 참조 송신원 부분집합을 사용하는 방법을 제안하였다. 완전 파형 역산은 반복적인 파동 전파 모델링을 통해 수행되며, 송신원 개수가 증가할수록 계산 시간이 증가하게 된다. 완전 파형 역산의 계산량을 줄이기 위한 기법들 중 하나로, 주기적 송신원 추출 기법을 사용할 수 있지만 이 경우 역산 초기부터 목적함수가 진동하며 수렴하기 때문에 수렴 판별에 문제가 생기게 된다. 이러한 문제를 해결하고자 본 연구에서는 주기적 송신원 추출 기법을 이용해 모델을 갱신하되, 고정된 참조 송신원 부분집합을 이용해 목적함수를 계산하는 방법을 제안하였다. Marmousi 속도 모델을 이용한 완전 파형 역산 예제를 통해 참조 송신원 부분집합을 이용하면 주기적 송신원 추출 기법을 사용하더라도 목적함수가 안정적으로 수렴할 수 있음을 확인하였다.

Keywords

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Fig. 1. (a) A cyclic-shot subsampling scheme using two subsets and (b) a cyclic-shot subsampling scheme using three subsets and a reference subset.

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Fig. 2. The Marmousi P-wave velocity model.

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Fig. 3. A shot gather from a source exploded at 4.8 km from the left.

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Fig. 4. (a) The initial velocity model and (b) the inversion result using all shots. The result was obtained after 322 iterations. (c) Velocity profiles extracted at 3.2, 4.8, and 6.4 km from the left. (d) The error history.

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Fig. 5. The inversion result using the cyclic-shot subsampling when the size of a subset varies from 19 to 20. The result was obtained (a) after 15 iterations and (b) after 500 Iterations. (c) The inversion result using the reference-shot subset when the size of the reference subset is 10 and that of the cyclic-shot subset varies from 9 to 10. The result was obtained after 500 iterations. (d) The error histories.

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Fig. 6. (a) The inversion result using the cyclic-shot subsampling when the size of a subset varies from 47 to 48. The result was obtained after 103 iterations. (b) The inversion result using the reference-shot subset when the size of the reference subset is 30 and that of the cyclic-shot subset varies from 17 to 18. The result was obtained after 500 iterations. (c) The error histories.

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Fig. 7. (a) The inversion result using the reference-shot subset when the size of the reference subset is 2 and that of the cyclicshot subset varies from 17 to 18. The result was obtained after 208 iterations. (b) The inversion result using the reference-shot subset when the size of the reference subset is 5 and that of the cyclicshot subset varies from 14 to 15. The result was obtained after 337 iterations. (c) Error histories when the size of the reference-shot subset is 2, 5, and 10. The total number of shots used per iteration varies from 18 to 20.

Table 1. Information on shot subsets and termination criteria of numerical examples. Ntotal is the total number of shots used per iteration, Ncyclic is the number of shots in the cyclic subset, and Nreference is the number of shots in the reference subset.

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