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This work addresses the crucial challenges of simulating ultrasonic inspections in welded parts. We focus on the simulation of radiated ultrasonic fields in welded materials, incorporating spatially varying anisotropy and damping properties. Using macroscale descriptions to capture variations in weld properties as a function of grain orientation, two simulation methods are evaluated: a ray method and a hybrid finite element solution within the CIVA software. Simple simulations validate both models, but complexities emerge in real-world scenarios, notably caustic phenomena and beam splitting due to specific grain orientations. The proposed hybrid FE model can therefore provide reliable reference solutions, even for 3D configurations, allowing the biases arising from radius approximations to be quantified. [ABSTRACT FROM AUTHOR]