Geophysical problems often involve Lagrangian particles that follow surrounding flows and record information about the system, such as the pressure and temperature path recorded in metamorphic rocks. These Lagrangian particles can be useful for constraining unknown parameters, such as their sources and the thermal and flow processes of the surrounding fluid. To use information about Lagrangian particles to constrain unknown parameters about the surrounding fluid in an inverse manner, we have developed a 4D-Var (four-dimensional variational) data assimilation for thermal convection in a particle-grid coupled system. Here we consider particles advected in a thermally convecting, highly viscous fluid that mimics geochemical tracers in the Earth’s mantle, and estimate time series of thermal and velocity fields only from the particle records, focusing on their high traceability in the laminar flow. We present preliminary 4D-Var results using a sufficient amount of synthetic particle position and velocity data. The 4D-Var run achieves a 60-Myr time reversal of thermal convection with a horizontal wavelength of 6,000 km, without using any temperature data. For smaller scale convection, the cost function tends not to decrease well, but with a shorter retrospective time domain or a large weight on early stage information, the reconstruction improves. While this work focuses on mantle dynamics, our framework has the potential to constrain thermal, flow, and mixing processes in any other laminar flow containing Lagrangian particles that record useful information.

Monitoring and detecting marine volcanic activities are key for scientific understanding and disaster prevention. However, this is difficult because they are hidden under water. Near Torishima Island in the Izu Islands, Japan, intensified seismic activity was observed during October 2023, including a mysterious tsunami-triggering earthquake on October 8 (UTC), which was considered to be linked to a volcanic activity. On October 20, 2023, aerial surveys confirmed an 80-km stretch of floating pumice near Torishima Island. This study conducted a Lagrangian back-tracking drift simulation using the ocean current data and surface wind data to trace the origin of the pumice while clarifying the theoretical basis of Lagrangian back-tracking from the Bayesian perspective. Results indicate that the pumice drifted southward from around extensional back-arc basins near Myojinsho Reef and Sumisujima Island approximately 3–5 days before its discovery. These findings are consistent with independent observations such as biological traces and the geochemical characteristics of sampled floating pumice, which is considered identical to that found on October 20 by an airplane. This indicates the presence of unknown volcanic activity around back-arc basins west of the major active volcanic zone. This study demonstrates the utility of combining drift simulations with geochemical and biological data to identify the sources of marine volcanic events, particularly in regions where direct observations are limited. The results of this study contribute to our understanding of volcanic mechanisms and their potential hazards.