## 1 Introduction  
Ultrasonic imaging of full matrix capture acquisitions using TFM (total focusing method [1]) or derived algorithms typically rely on the assumption that ultrasound propagates with constant (and usually isotropic) velocity within the part to be inspected. This assumption greatly simplifies the calculation of shortest travel times between a transmitting element and an observation point, which needs to be performed \(N_{\text{elements}}\times N_{\text{observation point}}\) times for typical reconstruction algorithms. However, the assumption of constant travel time breaks down within austenitic welds [2], in which a microstructure with large oriented austenitic grains causes local velocity differences, which affect the ultrasonic beam; it suffers from multiple deviations at grain boundaries, and sometimes is split into several beams, modifying the focusing properties significantly. If reconstructed ignoring the actual microstructure, the resulting image will inevitably fail to predict the correct defect location [3; 4]. Embedding material information into imaging algorithms involves calculating delay laws for the imaged domain, accounting for heterogeneous anisotropy [5]. Material information required for such calculations can be obtained from several sources, including the destructive examination (Electron Backscatter Diffraction--EBSD, metallography), ultrasonic inversion (within the ADVISE project, we have developed several techniques for determining the weld structure [6; 7; 8]), or weld formation simulation. This paper addresses the last mentioned approach, analysing the impact of a few weld formation model parameters from the ultrasonic imaging perspective. Thick austenitic welds are characterised by long columnar grains with locally preferential orientations. To model ultrasound propagation, one can either develop a model based directly on the measured microstructure (grain-scale) or use its homogenised counterpart [9]. It is common in the non-destructive evaluation (NDE) community to homogenise grains with similar orientations and create a macroscale description, replacing clusters of grains with a locally homogeneous anisotropic material (transversely isotropic) rotated according to the dominant orientations of grains. Such a description typically takes the form of a regular map, splitting the domain into square-shaped regions for which homogenised dominant orientation is specified. For most practical cases, a homogenisation scale of 2 mm is considered sufficient [9; 10]. The grain layout described above is responsible for two detrimental effects on imaging, beam deviation, and increased noise. Since the orientation of grains varies across the weld, the ultrasound no longer travels along straight paths. The complex, curved ray paths lead to misinterpretation of conventional inspections in which the position of the reflectors cannot be judged reliably any more. For imaging, where isotropic delay laws are traditionally assumed, defect signatures can be misplaced. The other effect, which is often dominant, is the reduction in the signal-to-noise ratio; as with unmatched delay laws, the TFM's beamforming is out of focus and spreads the energy of the scatterer across the surrounding area. Further complicated by grain noise, which is always present in coarse grain materials, the reduction in the signal-to-noise ratio (SNR) may bury the signature of interest below the noise floor. These two effects can be tackled by embedding material information into imaging. One way to do this is to precompute delay laws assuming a given grain orientation map for the weld under test and use these delay laws in TFM imaging. The first attempts to describe grain orientations used simple geometric representations, for instance, the single-angle symmetric arrangement in [11], or the multi-layer model [12]. The first flexible gold-standard model--the Ogilvy map--was proposed a few years earlier [13] and allowed for a continuous orientation variation to be modelled.