I spent the last week of March visiting the Institute of Seismology and Volcanology at the University of Hokkaido in Sapporo, finishing off a paper that was submitted to a special issue of the Bulletin of the Seismological Society of America (BSSA) on the Tohoku-oki tsunami of 11 March 2011. It is now posted here.
This work started last summer when Bre MacInnes was still at UW working with me on an NSF RAPID grant to perform simulations of this tsunami using our GeoClaw code. She’s now a postdoc in Sapporo and together with Adit Gusman (another postdoc there) and Y. Tanioka (director of the Institute), we compared 10 proposed sources for the tsunami by simulating the resulting wave using GeoClaw and comparing with observations. Each source is a model of the seafloor deformation that caused the tsunami. Dozens of similar (but far from identical) source models have been developed by different research groups, by performing some form of inversion based on some combination of seismic, tsunami, and GPS data. Some sources model the slip along the fault plane, 10s of kilometers below the seafloor, which we converted to seafloor deformation using the Okada model (based on a Green’s function solution to the equations of elastic deformation in a half space). Other groups directly modeled the seafloor deformation based primarily on tsunami data.
For each earthquake source, we compared results at 4 DART buoys (pressure gauges on the ocean floor) near Japan and in four locations along the coast, including the Sendai Plain and 3 communities further north on the Sanriku Coast. We found that the sources developed using tsunami data typically performed the best for tsunami modeling, perhaps not surprisingly. Many of the simulated results agreed quite well with observations. However, none of the sources gave good agreement everywhere and it remains to sort out what source is best for tsunami modeling. Of course the numerical model has its own limitations, in particular that the shallow water equations are solved, a good approximation in many cases but not perfect by any means and it would be interesting to study some of the differences between observation and simulation in more detail.
For some information on how the GeoClaw code has been validated on a number of test problems, and other papers on tsunami modeling and the software more generally, see the GeoClaw webpage.
In addition to the figures in the paper, we also created an electronic supplement of additional figures along with most of the raw data used in the simulations and comparisons. Until a few years ago, I had never worked with data from the real world (like most mathematicians) and it has been an interesting experience learning to work with large data sets, and thinking about the best way to archive and curate this data. Reproducibility in computational science research is one of my big interests these days, and this paper was a good case study for this. The journal BSSA encourages the submission of electronic supplements, and I found that the webpage format they provided was easy to work with. We’re also collecting all the simulation and data analysis codes in a Github repository.