Sensitivity kernels of infrasound travel times to atmospheric parameters: numerical developments, validation and tests cases

Infrasound, and more generally acoustic waves, are omnipresent in the atmosphere due to their intrinsic characteristics and a wide variety of sources. The propagation of these waves is strongly influenced by the properties of the propagation environment, such as the speed of sound and wind. Therefore, observing and studying these waves can reveal important details about the state of the atmosphere.

The concept of using infrasound to improve atmospheric modeling by exploiting the sensitivity of waveforms is illustrated in a preliminary investigation (Gerier et al., 2025). From a data assimilation technique perspective, our goal here is to investigate and extend further their work by adapting the sensitivity kernel of infrasound full waveform to the sensitivity kernel of infrasound arrival times.

Sensitivity of arrival times to a specific model corresponds to the Fréchet derivative of the difference between the arrival time of the observation and that of the synthetic infrasound. First, the synthetic infrasound is computed by solving the linearized Euler equation using finite differences discretization. Then, the Fréchet derivative is obtained by using the adjoint method, which requires solving an adjoint wavefield problem and cross-correlating the adjoint wavefield with the synthetic direct wavefield.

The validation of the arrival time sensitivity kernels is discussed, along with the effects and implication of source frequency. The explosion at the Hukkakero site in Finland is chosen as a case study. A comparison between the sensitivity of waveforms and travel times is also performed.