평면파 변환을 이용한 3차원 탄성파자료의 효과적인 2차원 완전파형역산
Effective 2D Full Waveform Inversion for 3D Seismic Data using Plane-Wave Transformation
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초록
완전파형역산은 정확한 파동방정식의 해에 의해 얻어진 예측자료와 관측자료와의 잔차를 줄여가며속도모델을 업데이트 시키는 자료처리 방법이다. 그러나 실제 현장자료는 3차원적 송신원에 의해 얻어지게 되어2차원 파동방정식을 이용한 2차원 역산을 수행하면 서로 다른 그린함수로 인해 역산 수행에 근본적인 문제가발생한다. 이 연구에서는 이러한 문제를 해결하기 위해 3차원 자료를 평면파자료로 변환하여 2차원 평면파 완전파형역산을 수행하는 방법을 제안하였다. 평면파자료는 1차원 그린함수를 따르는 해가 되므로 그린함수의 차이에 의한 문제가 발생되지 않고 이 방법을 적용 시 계산비용이 줄어드는 장점도 갖게 된다. 제안한 방법의 효용성을 확인하기 위해 3층 층서모델 및 3차원 SEG/EAGE 충상단층(overthrust) 모델에 적용하였고 수치 실험 결과평면파 완전파형역산이 성공적으로 수행됨을 확인하였다.
Abstract
Full waveform inversion (FWI) provides accurate velocity information of subsurface media. FWI can update velocity as reducing the residual between the observed and estimated data which can be obtained by solving wave equation. Therefore, when we carry out 2D FWI with 3D data acquired in a field, critical problems happen in FWI, because 2D and 3D wave equations have different green functions. To overcome the problem we suggest 2D plane-wave FWI method using plane-wave gathers, which are transformed from 3D data, as observed data. Since plane-wave data follow 1D green function, the differences of amplitude and phase do not occur, it means that we can implement FWI by using different dimension data. In addition, this method has advantage that computational cost is considerably reduced. To verifythe validity of this method, we applied it to 3 layer model and 3D SEG/EAGE overthrust model and obtained reasonable inversion results.
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