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Not bad (except for the white background) — looks like it’s using actual LaTeX behind the scenes to do the rendering. Beats trying to make sense of MathML, anyway.

Plan section through "pre-SPREE" tomographic model, built from Canadian and US data through August, 2009. This slice is at 250 km depth below the surface.

This is a slice through a 3-D tomography model I’ve been working on — basically, I’ve spent odd moments over the past few months measuring relative arrival times of earthquakes at various instruments in central Canada and the US. Red zones are regions where the waves travel more slowly than average, and blue zones are the converse, as determined by a rather lengthy computation that finds an image that matches all of the measurements from different directions as accurately as possible.

So what does it mean? Well, this is a look into the lithosphere — the layer below the Earth’s crust that participates in plate tectonics. So you’d think that the structure of the lithosphere would closely match that of the crust above (the grey lines), but it doesn’t. There are features that match crustal structures (like the little red zone marked “Nipigon”, above), and other features that don’t. Notably, the big blue blob I’m calling the Western Superior Anomaly is a lot smaller than the western portion of the Superior Province, the crustal region it underlies.

SKS splitting times for the same map region as above -- contours and colour scale are in seconds, triangles are measurement points.

There’s another, independent line of evidence indicating that the western Superior has something unusual underneath it: the contour map above. More measurements made from earthquakes here, this time looking at the effect of mantle fabric on polarized SKS waves. If the rock in the upper mantle (including the lithosphere) has a strong fabric to it, it will cause the incoming polarized wave to split into two waves that arrive at different times. The map above shows the time difference between the two — and, looking at the contours, it seems clear that the western Superior anomaly stands out in this way as well.

So, what does this all mean? Well, I’m working on that. Hopefully I’ll have something semi-sensible to say at AGU in a few weeks.

I can, at least, say something meaningful about the seismology. The best source for information on recent earthquakes is usually the USGS page. The basic parameters of an earthquake are time, location, magnitude, and source mechanism. Time is generally given in universal time code (UTC) rather than in any particular time zone. The location is given in three dimensions: latitude, longitude, and depth. Depth is the hardest of the three to measure accurately, but the value given (10 km) is relatively shallow — well within the crust. Shallower earthquakes are more likely to be damaging than deeper ones due to the shorter distance to the surface. This map puts the event in context with respect to other earthquakes in the region: Haiti’s actually west of the main subduction-zone seismicity — earthquakes are much more frequent elsewhere in the Caribbean. The fault yesterday’s earthquake was on is a strike-slip (horizontal motion, like the San Andreas) fault with left-lateral motion (if you stand on one side of the fault, the other side’s moving to the left).

The magnitude of the earthquake was, based on current estimates, a 7.0. That’s big, comparable to the 1989 Loma Prieta earthquake that did serious damage to San Francisco and environs. It’s not big enough to be all that rare on a global scale, however — a quick search of the ANSS catalog shows 145 events of magnitude 7.0 or greater since the beginning of 2000 (i.e. a bit over one per month). The earthquake magnitude scale is logarithmic, meaning that the Sumatran earthquake of 2004 (a 9.0) was roughly 100 times the size of this one. An earthquake’s effect on humans depends on a lot more than the magnitude, though — where it is in relation to populated areas is of critical importance, as are the response of local soils (soft ground can make matters worse) and the types of construction used.

Finally, there’s the source mechanism. It’s possible to work out, by looking at the waves radiated out in different directions, what the “radiation pattern” of energy transmitted by the earthquake was. There are different characteristic patterns for different types of fault motions. This earthquake’s pattern is characteristic of a slightly oblique strike-slip fault; based on the pattern, two different fault orientations are possible, but one (WSW-ESE) lines up with known fault traces and gives the expected left-lateral motion.

As I mentioned before, the earthquake showed up very strongly on the old analog seismograph we have as part of a museum display. The fancier digital instrument chose this opportune moment to play dead, but I obtained seismograms from an instrument operated by the Canadian National Seismograph Network that is located fairly close by.

The instrument in question records ground motion along three axes (N-S, E-W, and vertical); in the above plot I’ve rotated the horizontal components into radial (parallel to the path to the source) and transverse (perpendicular to the path to the source) components to show how different the result is. At this distance, four major wave types are observed: P and S waves, which pass through the Earth’s interior, and Love and Rayleigh waves, which travel along the surface. The surface waves are much lower in frequency and higher in amplitude than the body waves. P and S waves are also different in frequency and polarization, as we can see by zooming in:

Geophysics is a visual science. Nearly every paper I’ve written has started with the figures. The reason for this is that the end result of data analysis or calculation ends up making sense only as an image; the figures in my papers usually contain the results that the text seeks to obtain or interpret.

This dependence on imagery requires, like it or not, that I do some thinking about visual design and data presentation. The same information can often be presented several ways. Right now I’m putting together some results (collected by several people that I’ll credit properly in a future post) obtained using a measurement technique called shear-wave splitting. Skipping over what the measurement is, exactly (again for a later post), the ultimate result for a given seismometer station is two numbers: a direction (relative to north), and a magnitude (given in seconds). The map above uses the orthodox way of presenting this kind of information: double-headed[*] arrows oriented to follow the measured direction, with lengths scaled by the magnitude. This approach makes it easy to see how the splitting orientation relates to other features (such as the geological boundaries indicated by blue lines), but the arrows tend to overlap and obscure some of the spatial characteristics of the data (such as whether two points on opposite sides of the map have the same value).

Another way to do it is to separate the two:

Is this better, or worse? It does a better job of indicating that there’s a region in the centre of the map with high split times, which reinforces the point of the paper — at the same time, the azimuth is reduced to an abstraction, rather than drawing an angle as an angle.

In the paper I’m writing (actually an extended abstract for GeoCanada 2010), I think I’ll be using both — contours to show the extent, arrows to show the geological relationship. But maybe there’s a better graphical approach out there that I haven’t found yet.

As a postscript: I made these maps with a set of software tools called the Generic Map Tools, or GMT. They’re slightly obscure at times, but I find them better for my work than any GIS system I’ve fiddled with.

[*] Double-headed because the angle is out of 180 degrees rather than 360 — the method doesn’t distinguish between north-northwest and south-southeast.

(Yes, I’m thinking about reviving this blog.)

I’m presenting in this session on Monday afternoon, as is my graduate student. Poster sessions like this are always enjoyable, particularly since there’ll be a number of people I know presenting there, and several of them are also working on the Ontario lithosphere.

I’m also rather pleased with the figure above, which went into a poster I’m bringing. Essentially, it looks like a number of the structures in the Ontario model are correlated with subduction features detected in other studies, as well as with the linear feature previously attributed to the Great Meteor hotspot track; the question marks indicate newly detected features whose significance we’re going to have to figure out.

As only the city gives a meaning to the bleak landscape of the hermit, so the study, with its silence and its order, is simply the place where the oscillations of the seismographs are recorded.

(Italo Calvino, The Castle of Crossed Destinies, translated by William Weaver)

I think this quote’s going on my office door.

Superior Province tomography: The Superior Province is an Archean craton — that is, one of the oldest chunks of stable continent in the world — which makes up most of Ontario, along with a decent slice of Quebec and (buried under sediment) about half of Manitoba. The deep roots of these cratons (below the crust) are the subject of much interest, though the Superior has only really been looked at in piecemeal fashion.

Until now, that is. The FEDNOR array has put a coarsely-spaced set of seismic stations out on the Superior; thanks to two Stéphanes, we’ve been able to include data from temporary deployments in the region as well. The result is a 3-D image of seismic velocity beneath most of Ontario:

resulting from recording earthquake traveltimes at stations from FEDNOR/POLARIS, the Canadian National Seismograph Network, the Abitibi and TW~ST experiments, and (thanks to some digital archeology and the IRIS Data Management Centre) the older APT89 experiment. The overall coverage is pretty good (blacked-out areas are not well covered), and in these early results, there appears to be a major difference between the eastern (mostly red, i.e. seismically slow) and western (mostly blue, fast) regions of the Superior Province. A few more FEDNOR stations have just gone in, and will hopefully help close up that resolution hole in the middle; still, even what we have now is a pretty good-sized data set, representing (among other things) a lot of trvel-time picking work by Soo-Kyung Miong, the student who’s been working on this.

Soo also did SKS splitting analysis (a technique which detects directional fabric) at the same stations for her honours thesis; the splits at the western stations are stronger and more consistent in the east. A full presentation of this will go into a paper soonish (once again, it’ll be nice to have those new stations), but in the meantime, in collaboration with Ian and Dave, we’ve been looking at…

…Mantle Fabric in Eastern Ontario: There’s nothing like a journal special issue (with deadline) to make one write a paper in a hurry. This one combines the aforementioned SKS splitting in eastern Ontario with magnetotelluric measurements of geoelectric strike (another measure of fabric, this time in electrical rather than seismic properties) and some receiver function studies of individual stations (which I’ve mentioned before) in order to get an idea of how the fabric varies with depth. There’s no simple punch line, but here’s a map:

showing electrical strike directions (black) along with seismic fast-axis directions (red; lighter red arrows are Soo’s new results). They’re not the same, but they don’t seem to be uncorrelated, either. I still don’t entirely understand the guts of the magnetotelluric method, but watching Ian work on this has been instructive — hanging around smart people is never a bad thing.

The latter paper’s already submitted — I may put up a preprint at some point, if my co-authors don’t mind — and hopefully the other project will be a paper before the end of the year. Then it’ll be time for the next project — and I haven’t even mentioned the project my graduate student, Jinling Zhang, is working on, which is looking extremely promising.

Now I need to decide how much of this I can cram into AGU posters…