Abstract
Spatial growth patterns are natural recording media (NRMs) that preserve important historical information, which can be accessed and analyzed to reconstruct past environmental conditions and events. Here, we propose the Bayesian inversion method, which can reconstruct the evolution of target parameters from purely spatial data by extending data assimilation (DA), a method for integrating numerical simulations with time-series observations. Our method converts discrete spatial observation data to time-series data with the help of a law representing the NRM's time-evolution dynamics and Gaussian process regression, enabling us to directly compare the observations with a numerical simulation based on the DA framework. The method's effectiveness is demonstrated using a synthetic inversion problem, namely reconstructing the $\mathit{pressure}--\mathit{temperature}--\mathit{time}$ ($P--T--t$) path of a metamorphic rock from chemical composition profiles of its zoned minerals. The proposed method is broadly applicable to a wide variety of NRMs.
Highlights
Nature often records the dynamics of environmental parameters as structural patterns, which we call natural recording media (NRMs), just like digital pits in compact discs (CDs) and the grooves in vinyl records
We have proposed a method for reconstructing the time evolution of unknown parameters from spatial observation data based on a data assimilation framework
In conventional data assimilation (DA), a state-space model is constructed to relate a numerical simulation to temporal observations
Summary
Nature often records the dynamics of environmental parameters as structural patterns, which we call natural recording media (NRMs), just like digital pits in compact discs (CDs) and the grooves in vinyl records. Typical examples include tree rings, ice cores, lithological layers, otoliths, shells, human nails, and secular fatigue damage accumulated in materials. These structures grow over time, so each spatial position corresponds to a particular point in time. They preserve precious information, often unique direct evidence of the past physical and chemical conditions of the target system. That said, decoding the evolution of particular parameters from NRMs is difficult, because (1) the recorded data do not directly reflect the parameters we would like to estimate, and (2) temporal information has to be simultaneously estimated from the spatial structure.
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