Acoustic modeling of low-frequency seismic sources in transition zones: state of the art and challenges

Abstract Low-frequency marine seismic sources are becoming increasingly important for enhancing deep-target illumination and improving the stability of broadband imaging, particularly for Full-Waveform Inversion and quantitative imaging. This study investigates the modeling of a large-volume low-frequency marine source designed to radiate energy down to about 1 Hz. Unlike conventional air guns, this source operates in a distinct physical regime, generating a much larger bubble and a longer oscillation period. In deep water, field observations show that spherical lumped-parameter models already provide a robust first-order description of its acoustic signature. Because the Tuned Pulse Source (TPS) behaves as a single, nearly omnidirectional point source, it produces a simpler and more controlled wavefield than conventional air-gun arrays, creating favorable conditions for precise source characterization and predictive modeling. In shallow-water and transition-zone environments, the larger bubble size, stronger hydrostatic pressure gradients, buoyancy, and free-surface interaction motivate a more refined representation of source dynamics. These effects are expected to influence the low-frequency signature, particularly through stronger coupling between the source pulse and surface ghost reflections. The paper therefore evaluates the range of applicability of conventional spherical source models for such configurations and identifies the conditions under which higher-fidelity approaches can further improve source characterization. It also highlights the potential of Boundary Element Methods (BEM) to capture non-spherical bubble dynamics and more complex boundary interactions, while addressing the associated mathematical and numerical challenges. Overall, the study establishes a physics-based framework for progressively improving TPS modeling in shallow-water settings and supports future experimental validation in transition-zone applications.