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.

The establishment of the High Sensitivity Seismograph Network (Hi-net) in Japan has led to the discovery of deep low-frequency tremors. Since such tremors are considered to be related to large earthquakes adjacent to tremors on the same subducting plate interface, it is important in seismology to investigate tremors before establishing modern seismograph networks that record seismic data digitally. We propose a deep learning method to detect evidence of tremors from seismogram images recorded on paper more than 50 years ago. In our previous study, we constructed a convolutional neural network (CNN) based on the Residual Network (ResNet) structure and verified its performance through learning with synthetic images generated based on past seismograms. In this study, we trained the CNN with seismogram images converted from real seismic data recorded by Hi-net. The CNN trained by fine-tuning achieved an accuracy of 98.64% for determining whether an input image contains tremors. The Gradient-weighted Class Activation Mapping (Grad-CAM) heatmaps to visualize model predictions indicate that the CNN successfully detects tremors without affections of a variety of noises, such as teleseisms. The trained CNN was applied to the past seismograms recorded at the Kumano observatory, Japan, operated by Earthquake Research Institute, The University of Tokyo. The CNN shows the potential to detect tremors from past seismogram images for broader applications, such as publishing a new tremor catalog.