Full Waveform Inversion (FWI) is a successful and well-established inverse method for reconstructing material models from measured wave signals. In the field of seismic exploration, FWI has proven particularly successful in the reconstruction of smoothly varying material deviations. In contrast, non-destructive testing (NDT) often requires the detection and specification of sharp defects in a specimen. If the contrast between materials is low, FWI can be successfully applied to these problems as well. However, so far the method is not fully suitable to image defects such as voids, which are characterized by a high contrast in the material parameters. In this paper, we introduce a dimensionless scaling function $\gamma$ to model voids in the forward and inverse scalar wave equation problem. Depending on which material parameters this function $\gamma$ scales, different modeling approaches are presented, leading to three formulations of mono-parameter FWI and one formulation of two-parameter FWI. The resulting problems are solved by first-order optimization, where the gradient is computed by an ajdoint state method. The corresponding Fr\'echet kernels are derived for each approach and the associated minimization is performed using an L-BFGS algorithm. A comparison between the different approaches shows that scaling the density with $\gamma$ is most promising for parameterizing voids in the forward and inverse problem. Finally, in order to consider arbitrary complex geometries known a priori, this approach is combined with an immersed boundary method, the finite cell method (FCM).
翻译:完全波形反转 (FWI) 是利用测量的波浪信号重建材料模型的成功和既定的反向方法。 在地震勘探领域,FWI已证明在重建顺利的不同物质偏差方面特别成功。 相反,非破坏性测试通常要求检测和具体确定标本中的明显缺陷。 如果材料之间的对比较低,FWI也可以成功地应用到这些问题。 但是,迄今为止,该方法并不完全适合图像缺陷,例如空虚,其特点是物质参数的对比性很高。在本文中,我们引入了一个无尺寸的缩放功能$\gamma$,用于模拟前向和反向的卡通波方方方程式问题。根据哪个物质参数,这一功能是美元/gammama$的尺度,提出了不同的模型方法,导致三个单参数FWIWI的配方,一个2度FWI的配方。 由此产生的问题通过一级优化方法解决,在那里,以一个jdoint状态方法计算梯度。我们引入的Frchelch GS内的相应的缩放值缩缩缩缩缩法是每个FMFI 的缩略法, 和最小化法的缩略法是最后的缩缩略法。 。 的缩略法是用来推测法的缩进。