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It is a general problem in geoscience to estimate the time-series of velocity and temperature fields for a fluid based on limited observations, such as the flow velocity at the fluid surface and/or a temperature snapshot after flow. In this study, an adjoint-based data assimilation method (also known as 4-D variational data assimilation) was used to reconstruct the thermal convection in a highly viscous fluid (e.g. Earth's mantle) to investigate which observations constrain the thermal convection and how accurately the convection can be reconstructed for different wavelengths. The data assimilated to the adjoint-based model were generated synthetically from forward models with convecting cells of different length-scales. Based on the surface velocity and temperature snapshot, our simulations successfully reconstructed thermal convection over 50 Myr in the case that the wavelength of the convective cells is sufficiently large. We obtained two main results from this parametric study. (1) When we only considered instantaneous thermal structure fitting in the cost function, the convection reconstruction tended to fail. However, there are some cases where the laminar thermal convection can be reconstructed by assimilating only the velocity along the fluid surface. (2) There is a limit to the reconstruction of thermal convection in the case that the convecting cells are small (∼1000 km for a 50 Myr reconstruction). We propose that (1) is related to the balance of forces due to the thermal buoyancy and viscous stress around the thermal anomalies and (2) is related to how information is preserved (i.e. how the previous thermal structure is maintained in the observable state throughout the convection process). The results enable the use of geological records to estimate time-series of velocity and temperature in Earth's deep interior, even though the records may only contain information from shallow parts of Earth. [ABSTRACT FROM AUTHOR]

To deeply understand various geodynamic processes, including volcanic activities and earthquakes, it is essential to extract detailed information about Earth materials, such as lithology and geofluid, from geophysical, petrological, and geochemical observations of Earth's interior. We developed a Bayesian probabilistic framework that can estimate the lithology and geofluid type (aqueous fluid or melt), geofluid amount (porosity), and parameters related to the fluid geometry (aspect ratio and critical fluid fraction related to connectivity) from P‐wave and S‐wave seismic velocities and electrical conductivity data obtained from geophysical tomography. By conducting synthetic inversion tests, we showed that methods based on a joint probability distribution, which simultaneously determines all parameters, sometimes fail to narrow the number of possible answers from 78 lithologies (e.g., basalt, granite, and eclogite) × two geofluid type (melt or aqueous fluid) candidate sets. This failure is derived directly from the difficult nature of inversion problems with relatively large data uncertainties. The proposed method uses a marginalization technique that first estimates lithology and geofluid type and then quantifies geofluid parameter values, which can narrow the probable lithology, geofluid type, and geofluid parameter sets in many cases. In addition, the computational cost of the proposed marginalization method is comparative to a former joint‐estimation method, which is theoretically identical to a previous heuristic method based on the least squares method. Therefore, the marginalization method is useful for geophysical data analyses that involve large amounts of observational data with relatively large uncertainties. Plain Language Summary: To understand dynamic phenomena, such as volcanic activity and earthquakes, quantitative information about the structure of Earth's interior from geophysical, petrological, and geochemical datasets should be extracted. We propose a method to estimate parameters related to rock type, fluid type, fluid amount, shape, and connectivity from seismic wave velocity and electrical conductivity data using a probabilistic method called Bayesian inference. We conducted a test using artificially generated geophysical observational data to verify the effectiveness of this method. We found that determining the rock type and fluid type first and then estimating the remaining parameters is often more accurate for problems with relatively large amounts of observational noise compared to determining all parameters simultaneously. The proposed method can be used for 3D visualizations of Earth's interior. Key Points: We propose a probabilistic inversion method that estimates lithologies & liquid properties from seismic velocity & electrical conductivityA synthetic inversion test showed that the method using marginalization often recovers the true model more accurately than previous methodsThe flexibility of the Bayesian approach contributes to accurate estimations by incorporating a priori knowledge of geology [ABSTRACT FROM AUTHOR]

Detection of sodium-salt-rich ice grains emitted from the plume of the Saturnian moon Enceladus suggests that the grains formed as frozen droplets from a liquid water reservoir that is, or has been, in contact with rock (1,2). Gravitational field measurements suggest a regional south polar subsurface ocean of about 10 kilometres thickness located beneath an ice crust 30 to 40 kilometres thick (3). These findings imply rock-water interactions in regions surrounding the core of Enceladus. The resulting chemical 'footprints' are expected to be preserved in the liquid and subsequently transported upwards to the near-surface plume sources, where they eventually would be ejected and could be measured by a spacecraft (4). Here we report an analysis of silicon-rich, nanometre-sized dust particles (5-8) (so-called stream particles) that stand out from the water-ice-dominated objects characteristic of Saturn. We interpret these grains as nanometre-sized Si[O.sub.2] (silica) particles, initially embedded in icy grains emitted from Enceladus' subsurface waters and released by sputter erosion in Saturn's E ring. The composition and the limited size range (2 to 8 nanometres in radius) of stream particles indicate ongoing high-temperature (>90°C) hydrothermal reactions associated with global-scale geothermal activity that quickly transports hydrothermal products from the ocean floor at a depth of at least 40 kilometres up to the plume of Enceladus., Dust dynamics provide diagnostic information about the origin of the observed dust populations. The dynamical properties of Saturnian stream particles show characteristics inherited from Saturn's diffuse E ring (7). Considering [...]