Recent research in real-time tsunami early warning can be broadly classified into two approaches. The first involves the use of seismic and regional geodetic data to calculate the tsunami wavefield indirectly through the estimation of earthquake source parameters. The second directly reconstructs the tsunami wavefield using data assimilation of ocean-bottom pressure sensor data such as those from DONET and S-NET (Maeda et al. 2015, Gusman et al. 2016). Data assimilation interpolates between the numerical solution and the observations to make the forecast more consistent with real data. Currently, the most popular method for forecasting the waveform is optimal interpolation, which uses a Kalman filter (KF) like approach, but holds the Kalman gain matrix fixed to reduce the runtime. This approach, coupled with tsunami Green’s functions, is very efficient and generates useful predictions. Here, we demonstrate that more accurate and stable forecasts can be obtained using the ensemble KF (enKF), a more computationally efficient variant of KF, in which the gain matrix is updated according to the physical model and the evolution of the error covariance matrix. The ensemble representation is a form of dimensionality reduction, in that only a small ensemble is propagated, instead of the joint distribution including the full covariance matrix. This method also provides a means to obtain the probability distribution of the forecast at each grid point location. We use a scenario tsunami in the Cascadia subduction zone, generated from a 2D fully-coupled dynamic rupture simulation (Lotto et al., submitted 2018). Randomly perturbed tsunami wave height data is used in the assimilation process, as we propagate the wave using a 1D linear shallow water code on a staggered grid. Better waveform agreement is achieved even in the early stages of assimilation, with much less fluctuation compared to optimal interpolation. We also explore spatial and temporal aliasing effects, in terms of the relation between observation station spacing and wavelength, as well as between assimilation and forecast time intervals. Although enKF is computationally more expensive, we are working on a fast, parallelized GPU implementation, which will significantly reduce the runtime, taking us a step closer to reliable real-time tsunami early warning.

Explosive volcanic eruptions radiate seismic waves as a consequence of pressure and shear traction changes within the conduit/chamber system. Kinematic source inversions utilize these waves to determine equivalent seismic force and moment tensor sources, but relation to eruptive processes is often ambiguous and nonunique. In this work, we provide an alternative, forward modeling approach to calculate moment tensor and force equivalents of a model of eruptive conduit flow and chamber depressurization. We explain the equivalence of two seismic force descriptions, the first in terms of traction changes on the conduit/chamber walls, and the second in terms of changes in magma momentum, weight, and momentum transfer to the atmosphere. Eruption onset is marked by a downward seismic force, associated with loss of restraining shear tractions from fragmentation. This is followed by a much larger upward seismic force from upward drag of ascending magma and reduction of magma weight remaining in the conduit/chamber system. The static force is upward, arising from weight reduction. We calculate synthetic seismograms to examine the expression of eruptive processes at different receiver distances. Filtering these synthetics to the frequency band typically resolved by broadband seismometers produces waveforms similar to very long period (VLP) seismic events observed in strombolian and vulcanian eruptions. However, filtering heavily distorts waveforms, accentuating processes in early, unsteady parts of eruptions and eliminating information about longer time scale depressurization and weight changes that dominate unfiltered seismograms. The workflow we have introduced can be utilized to directly and quantitatively connect eruption models with seismic observations.