The tsunami data assimilation method enables tsunami forecasting directly from observations, without the need of estimating tsunami sources. However, it requires a dense observation network to produce desirable results. Here we propose a modified method of tsunami data assimilation for regions with a sparse observation network. The method utilizes interpolated waveforms at virtual stations. The tsunami waveforms at the virtual stations between two existing observation stations are estimated by shifting arrival times with the linear interpolation of observed arrival times and by correcting the amplitudes for their water depths. In our new data assimilation approach, we employ the Optimal Interpolation algorithm to both the real observations and virtual stations, in order to construct a complete wavefront of tsunami propagation. The application to the 2004 Sumatra‐Andaman earthquake and the 2009 Dusky Sound, New Zealand, earthquake reveals that addition of virtual stations greatly helps improve the tsunami forecasting accuracy.

Abnormal volcanic earthquakes occurring near the volcanic island of Torishima, south of Japan, sometimes generate relatively larger tsunamis compared to the seismic magnitudes. They have a non-double-couple focal mechanism known as compensated linear vector dipole. The unusual earthquake source mechanism poses difficulties in traditional tsunami forecasting method based on seismic parameters. Tsunami data assimilation, a method of tsunami forecast using offshore tsunami observation data and numerical model, avoids the complexities and uncertainties in the tsunami source estimation and makes a tsunami early warning at coastal points of interest. Along Nankai trough, many offshore bottom pressure gauges are installed, and the data are transmitted in real time through submarine cables. Previous synthetic experiments have demonstrated the capability of the data assimilation approach for tsunami forecasting. In this paper, we report the successful application of the tsunami data assimilation to the cabled ocean bottom pressure gauge data for the first time. We assimilated the tsunami data recorded on ocean bottom pressure gauges to retroactively forecast the tsunamis of the 2015 Torishima earthquake. Comparison of the forecasted and observed waveforms at two coastal tide gauges (Kushimoto and Tosashimizu) confirmed that our method could forecast the tsunami amplitude and arrival time accurately, merely based on offshore tsunami observations. We also investigated the relationship between the number of observational stations used for assimilation and the forecasting accuracy and determined which stations were more important in data assimilation.

A tsunami was triggered in the North Pacific Ocean by the 2021 Alaska earthquake (M 8.2) on July 29. We studied the source properties and resonance characteristics of the tsunami event using observed records from offshore tsunameters and coastal tide gauges as well as numerical simulation. Spectral analyses were conducted on records at tsunameters and tide gauges. We reconstructed the tsunami source spectrum by calculating the ratio of tsunami spectra to the background spectra of these stations. Based on the source spectrum, we estimated the source size of the 2021 Alaska earthquake to be 332 km (length) × $\times $ 256 km (width), which was generally consistent with the source model proposed by the United States Geological Survey using seismological approaches. In addition, we also performed spectral analyses of the tsunami wavefield in a region of interest, including the Aleutian Islands and the Alaska Peninsula. Standing wave systems were found south of the Alaska Peninsula and the Aleutian Islands. The Aleutian Islands prevent the propagation of tsunami oscillations. Only a small portion of energy propagates through the archipelago from the main part of the Pacific Ocean to the Bering Sea.

Summary Ensemble methods have been applied successfully in assisted history matching and in production optimization. In history matching, the ensemble Kalman filter (EnKF) has been used to estimate the values of hundreds of thousands of variables from various types of data. In production optimization, an ensemble-based method has been used to estimate optimal control settings for problems with thousands of control variables. In both cases, relatively small numbers of random realizations are used to compute update directions for improving estimates. In this paper, we illustrate the application of the ensemble-based optimization on two fairly complex problems that would be difficult to handle by other methods. In the first example, we show its application to optimize inflow-control-valve (ICV) settings on two horizontal wells in a sector model of 200,000 cells. One hundred layers were used in the reservoir model to capture geological heterogeneity. The two wells were drilled parallel to the edgewater boundary. The optimization objective in this example is to minimize cumulative water production over a 10-year production period while maintaining a constant liquid-production rate. Results after only five optimization iterations with improved control-valve settings showed a 50% reduction in cumulative water production. The fully automated optimization process was completed within a few hours under a parallel-computing environment. The ensemble-based method was also applied successfully to a 3D case consisting of 10 multilateral wells with ICVs installed at each lateral junction. The interaction of various laterals is difficult to visualize, but the optimization algorithm was again successful in reducing water production. In this example, we demonstrate that proper choice of control variables can be important to the success of the optimization.