hawen: time-harmonic wave modeling and inversion using hybridizable discontinuous Galerkin discretization

Abstract

Many applications such as seismic and medical imaging, material sciences, or helioseismology and planetary science, aim to reconstruct properties of a non directly accessible or non-visible interior. For this purpose, they rely on waves whose propagation through a medium interrelates with the physical properties (density, sound speed, etc.) of this medium. The methodology for imaging with waves comprises of two main stages illustrated in Figure 1. In the data acquisition stage (Figure 1a), the medium response to probing waves is recorded (e.g., seismic waves from Earthquakes recorded by ground network). In the second stage, we rely on a reconstruction procedure which iteratively updates an initial model of physical parameters, so that numerical simulations approach the measurements (Figure 1b). This procedure is employed, for instance, for seismic (reconstruction of subsurface layers) and medical (disease diagnostic) imaging, see the introduction of Faucher & Scherzer (2020) and the references therein.

Quantitative inverse problem in visco-acoustic media under attenuation model uncertainty

“…The computation of the gradient is performed with the adjoint-state method ( [54,52,4]) specifically derived for the HDG discretization in [25]. For the two and three dimensional computational experiments that are carried out in the following sections, we use the open-source software hawen 1 , [20]. The precise computational cost is further discussed in Subsection 5.4…”

“…The following experiments have all been realized using software hawen, [20], see Footnote 1. We further detail the computational cost of the 2D and 3D reconstructions in Subsection 5.4.…”

Diffraction Tomography, Fourier Reconstruction, and Full Waveform Inversion

“…Our FWI-based reconstruction uses an iterative Newton-type method on an L 2 distance between data and simulations. For the discretization of the resulting partial differential equations, we use the hybridizable discontinuous Galerkin method (HDG), [8,18], and the open-source parallel software hawen 1 , [14].…”

“…In this section, we numerically compare the forward models presented above. For the discretization of the partial differential equation, we use the hybridizable discontinuous Galerkin method (HDG), [8,18], and the open-source parallel software hawen, see [14] and footnote 1. It is further employed to carry out the reconstruction with FWI in Section 6.1.…”

“…Furthermore, we incorporate white Gaussian noise in the simulated data, with a signal-to-noise ratio of 50 dB. In addition, for the inversion experiments with FWI which use the same software as the data generation (hawen, see [14] and footnote 1), the computational setup for modeling and inversion use different discretization mesh and order of polynomials.…”