Full waveform inversion (FWI) is an iterative identification process that serves to minimize the misfit of model-based simulated and experimentally measured wave field data, with the goal of identifying a field of parameters for a given physical object. The inverse optimization process of FWI is based on forward and backward solutions of the (elastic or acoustic) eave equation. In a previous paper [1], we explored opportunities of using the finite cell method (FCM) as the wave field solver to incorporate highly complex geometric models. Furthermore, we demonstrated that the identification of the model's density outperforms that of the velocity -- particularly in cases where unknown voids characterized by homogeneous Neumann boundary conditions need to be detected. The paper at hand extends this previous study: The isogeometric finite cell analysis (IGA-FCM) -- a combination of isogeometric analysis (IGA) and FCM -- is applied for the wave field solver, with the advantage that the polynomial degree and subsequently also the sampling frequency of the wave field can be increased quite easily. Since the inversion efficiency strongly depends on the accuracy of the forward and backward wave field solution and of the gradient of the functional, consistent and lumped mass matrix discretization are compared. The resolution of the grid describing the unknown material density is the decouple from the knot span grid. Finally, we propose an adaptive multi-resolution algorithm that refines the material grid only locally using an image processing-based refinement indicator. The developed inversion framework allows fast and memory-efficient wave simulation and object identification. While we study the general behavior of the proposed approach on 2D benchmark problems, a final 3D problem shows that it can also be used to identify voids in geometrically complex spatial structures.

翻译：全波形反演(FWI)是一种迭代识别过程，用于最小化基于模型模拟与实验测量的波场数据之间的失配，目的是识别给定物理对象的参数场。FWI的反向优化过程基于（弹性或声学）波动方程的正向和反向求解。在先前论文[1]中，我们探索了使用有限元法(FCM)作为波场求解器来整合高度复杂几何模型的可行性。此外，我们证明了模型密度识别优于速度识别——特别是在需要检测具有齐次纽曼边界条件的未知空洞时。本文延伸了先前研究：将等几何有限元分析(IGA-FCM)——等几何分析(IGA)与FCM的组合——应用于波场求解器，其优势在于可以较容易地提高多项式阶数以及随之而来的波场采样频率。由于反演效率强烈依赖于正反向波场解及泛函梯度的精度，本文对一致质量矩阵与集中质量矩阵离散化进行了比较。描述未知材料密度的网格分辨率与节点跨度网格解耦。最后，我们提出了一种自适应多分辨率算法，该算法使用基于图像处理的细化指标仅在局部细化材料网格。所开发的反演框架实现了快速且内存高效的波场模拟与目标识别。通过在二维基准问题上研究该方法的通用行为，最终三维问题表明该方法也可用于识别几何复杂空间结构中的空洞。