# Measuring the height of ocean waves with seismometers

As you read these lines, the ground below you is moving up and down every few seconds by a few micrometers at most, due to waves in the ocean. This very small motion, a tenth of the width of a hair, and its relation to waves have been known for nearly a century. Its amplitude increases when storms are present in the nearest oceans. What is new, and just published in the Journal of Geophysical Research, is that we now know exactly under what conditions this "seismic noise" is made by waves, and where seismic stations on may be used to measure waves.
This result opens the way to a more quantitative use of old seismic records, which go much further back in time than wave measurements at sea, and the monitoring of waves in poorly instrumented regions of the world ocean, in particular the Southern Hemisphere.

The full paper is available at on the AGU website or here.
let us take one example: we use the seismic station in Berkeley to estimate the wave heights offshore of San Francisco. As others have done before, we used one month of wave measurements to find an empirical link between seismic and wave signals. It works pretty well, except for a few events, in particular on January 26 (this date is marked by the blue star): the wave height did not exceed 5 m, and this method gives 7.2 m. In fact, most of the winter time seismic noise is associated to waves reflected from the coast, but on that occasion noise is instead caused by swells from a North Pacific storm interacting with wind waves from a local storm. Similar events were also causing large errors back in the 1970s, when seismic stations were deployed in Oregon to measure waves off the U.S. West Coast.

The novelty of our method for analysing seismic data is that we use a numerical wave model to compute the source of seismic noise: in order to estimate waves from noise, we first estimate noise from waves. It may sound silly because if we know waves to begin with, why should we estimate them from seismic data? Well, the trick is that we do not need to know them very accurately.
And this model tells us when these anomalous events occur for which a lot of noise is made by small waves, contrary to the general trend of a larger noise
coming from larger waves. The other benefit of using a wave model is that we can also estimate where the seismic noise is generated and thus understand where the method works. For seismic data in California, we are lucky to have noise which mostly comes from the same region along the coast (red area in the map shown here). Because the waves are almost the same in that area we can compare the seismic estimate from a single buoy in the ocean.

The model has also told us that, contrary to winter months, the summer noise has nothing to do with coastal reflection, contrary to previous beliefs.

Looking at other regions of the world, it can be difficult to estimate a wave height because the sources of noise jump around a very large area. This is the case for Western Europe, as illustrated below. Noises recorded in Scotland can come from a very large area in the Atlantic ocean. We can define an average wave height over that area using satellite data, but the typical error of that estimation is fairly large, more than 20% for a daily mean wave height.

In that case the most useful use of seismic noise may not be in the estimation of wave heights but rather in the comparison of the model for seismic noise with the measured seismic noise, which is very usfeful for detecting spurious trends in the model results: for example we could find that the wave heights are increasing according to the model but this may be due to a difference in wind measurement techniques that change the modelled winds used to drive the wave model.