점탄성 매질의 특성을 바탕으로 개선된 스폰지 경계조건을 활용한 탄성파 모델링
Seismic Wave Modeling with an Improved Sponge Boundary Condition Considering Viscoelastic Behavior
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모델 경계에서 생성되는 인위적인 파를 감쇠시켜 제거하는 흡수 경계조건인 스폰지 경계조건(SBC, sponge boundary condition)은 적용성이 낮아 탄성파 모델링에서 많이 사용되지 않았다. SBC 는 점탄성 매질에서의 고유감쇠를 나타내는 방정식과 유사한 형태를 가지고 있으나 다른 양상을보여준다. 이 연구에서는 이러한 점에 착안하여 고유감쇠와 유사한 특징을 갖는 새로운 형태의SBC를 제안한다. 기존 SBC는 주파수에 상관없이 감쇠의 크기가 일정한 반면, 새로운 SBC는 고주파수에 강한 감쇠가 적용된다. 여러 예제를 통해 이러한 특성을 분석하였다. 다른 흡수 경계조건인PML(perfectly matched layer)과 기존 및 새롭게 제안된 SBC를 비교한 결과, SBC가 PML과 비슷한정도의 성능을 내기 위해서는 더 두꺼운 흡수영역이 필요하지만, SBC는 계산을 효율적으로 만드는 장점이 있다는 것을 확인하였다. 또한, 새로운 SBC는 그 특성 상 가변적인 크기의 격자를 사용할수 있는데, 이를 통해 SBC의 계산 상의 효율성을 보전하면서도 PML과 비슷한 수준의 성능을 낼 수있음을 보여주었다.
Abstract
The sponge boundary condition (SBC), an absorbing boundary condition, has not been discussed considerably; additionally, it has not been commonly used owing to its low applicability. Although the SBC is similar to the equation describing intrinsic attenuation in viscoelastic media, its behavior differs from the viscoelastic case. Herein, we present a new form of the SBC, which shows similarities with intrinsic attenuation. We describe the characteristics of the conventional and new SBCs with some numerical examples. By comparing the SBCs with the perfectly matched layer (PML) boundary condition, we found that the SBCs required broader damping areas than the PML to suppress artificial reflections; however, the SBCs could compensate for this deficiency with computational efficiency. The new SBC allows using variable-sized grids for damping areas, which substantially improves the performance of the SBC to be comparable to the PML while partially preserving computational efficiency
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