  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.
