Estimating Young's moduli based on ultrasound and full-waveform inversion

Simon Schmid, Carmen Hachmann, Christian Boehm, Lion Krischer, Alexander Mendler, Jochen Kollofrath, Christian U. Grosse

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


Ultrasound is commonly utilized to determine the dynamic Young's moduli for estimating material deterioration or quantifying material parameters. This is either done with a resonance frequency analysis or ultrasound for rock or concrete specimens in geophysics or civil engineering. For ultrasound, these are typically cylindrical specimens measured in a through-transmission arrangement. However, this method presents some challenges, such as the need to accurately determine the onset of each wave mode and to calibrate system latency. To overcome these challenges, this study introduces a novel method that utilizes wavefield simulation and full-waveform inversion to estimate p- and s-wave, also called compression and shear wave, velocities. Where the traditional method requires two measurements, this innovative approach requires only one measurement with a single p-wave transducer. The s-wave velocity is estimated considering mode conversions within the specimen. High-fidelity ultrasound simulations are necessary for this approach. For that reason, the spatially distributed excitation of the ultrasound transducer is characterized by a laser Doppler vibrometer measurement. This led to a good estimate of the directivity pattern of the ultrasound transducer. The inverse problem for determining p- and s-wave velocity was solved successfully using a suitable misfit or cost function, the so-called graph-optimal-transport misfit. The specimens for the proof of concept study include six different metals. The precision of the estimated velocities using full-waveform inversion was compared with manual picking. As the simulated and measured waveforms matched well, this study can be seen as a starting point for material parameter determination for more complex geometries and heterogeneous materials using full-waveform inversion.

Original languageEnglish
Article number107165
StatePublished - Jan 2024


  • Directivity pattern
  • Full-waveform inversion
  • Inverse problem
  • Simulation
  • Ultrasound
  • Ultrasound transducer calibration
  • Young's modulus


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