## Seismic tomography: the easy way

When I was an undergrad, I had to take a year of geophysics, and on the first day, the professor explained that geophysics meant finding things underground without digging.  The rest of my lab group here at the UW are all marine geophysicists, and they routinely have to find things underground without digging, but with the added complication of having to get through a couple of kilometers of water, too.

You may remember my interview with Rob Weekly a few weeks back. This week’s interview is with my office-mate, Dax Soule. Dax studies marine geology and geophysics in the School of Oceanography at the University of Washington. Like Rob, he focuses on active source seismology. In fact, he’s looking at some of the same data as Rob, just different parts. And since we already went over a lot of the basic background in Rob’s post, I’m going to jump right into some fun tomography stuff. In a nutshell, tomography means building up a 3D picture of what’s underground by measuring how long it takes for seismic waves to travel through. In tomography, you’re not sampling the material directly, but you’re measuring how the seismic velocity varies. Seismic velocity is a measure of how quickly a seismic wave can travel through a certain type of rock, so if you know the velocity structure you can make inferences about the geological structure.

Imaging the earth’s crust

When you’re doing seismic tomography, it’s a bit like peeling back the layers of an onion: you have to figure out the shallow stuff before the deep. Rob’s work focused on obtaining a three-dimensional seismic velocity structure from the seafloor down to about 2.5-3 km depth. Dax is taking Rob’s results and extending downward to include the entire depth of the crust. He’s looking between the seafloor and the Mohorovicic discontinuity, or the “Moho”, which is the boundary between the earth’s crust and the mantle.

In seafloor maps of the region, you can see that there’s a bathymetric high – a plateau where the water depth is shallower than the surrounding seafloor. A seismic reflection study a few years back [1] showed that this plateau likely corresponds to a thickening of the oceanic crust at this location. Dax’s tomography work will help to clarify exactly what’s going on, and will give a more detailed picture of how the crustal thickness varies in the area.

Dax explained that measuring crustal thickness variations near a mid-ocean spreading center can tell you about how that crust was produced – was a episodic or constant? And where was the source of new crust – was it on the axis of the ridge, or off-axis?

How the experiment works

Here’s a little cartoon showing the basic geometry of the seismic experiment.

A seismic source is generated near the sea surface, and the energy travels through the water column and into the sea floor. Once in the earth’s crust, the energy is converted into to types of waves: primary waves (p-waves) and secondary waves (s-waves). There are many different types of paths that these waves can take as they travel through the earth, and each type of path is known as a “phase”. In the above figure, the two phases that are shown are Pg and PmP. Rob used the Pg phase arrivals to image the upper portion of the crust. Dax looks at the PmP phases, which are the ones that bounce off the Moho.

Dax goes through the data and manually picks out the PmP phase arrival times. This part of the job is not the most exciting, but someone’s got to do it! Fortunately, all that work does pay off, and once Dax has his picks, he can start digging into the tomography part of his work.

Five easy steps
Here’s a handy-dandy summary of the steps that Dax goes through to build up a tomographic inversion.

So that’s what my office-mate does… good to know!  Dax is still working through the data and the very complex inversion code, so stay tuned for a future post on what he finds deep in the crust, and what the crustal thickness can tell us about seafloor production at the Endeavour Ridge.

Reference
[1] Carbotte, Suzanne M., Mladen R. Nedimović, Juan Pablo Canales, Graham M. Kent, Alistair J. Harding, and Milena Marjanović. “Variable crustal structure along the Juan de Fuca Ridge: Influence of on‐axis hot spots and absolute plate motions.” Geochemistry, Geophysics, Geosystems 9, no. 8 (2008).

## Scrappy stray dog

Steph and Ian found a dog!  And can’t find its owner.  So they’ve taken it in for the time being.  He’s very sweet, and seems to get along great with people… as long as he has met them before.  He’s SO skinny and malnourished.

## Congrats Rob!!

Rob Weekly successfully completed his general exams today, and is officially a PhD candidate!  Awesome!!  Congratulations, Weekly!

## Last day of inverse theory :-(

Today was our last inverse theory class.  We didn’t have time to cover the conjugate gradient method, which was too bad, I was really hoping we would get to that stuff.  One of our lab group’s weekly readings was on the double-differencing technique for earthquake location.  In it, they described using a conjugate gradient-type method called LSQR.   It’s supposed to allow you to avoid inverting a giant matrix when solving inverse problems.  From my very basic understanding, it finds the answer in a sort of iterative way, by making successive guesses to find the minimum in some objective surface.  The good news is that Matlab has a canned lsqr function, so I could just try it out and see for myself.  Although the canned function can be a bad thing, because then you can just treat it like a black box.

## Streamlines and statistics

I finally, finally downloaded R today.  I’ve been meaning to check it out for ages.  I only spent about 10 minutes on it once I had it downloaded though – things are too busy to be playing with a new toy.  Next week is finals week.  Probably best to work on the things that have deadlines in the next 7 days.  Particularly those things which require me to give presentations in front of people.  Turns out that the prospect of public humiliation is a pretty decent motivator, actually.  I’ve been working away pretty diligently on getting those projects finished.

## Molly Moon’s and more inverse theory

It was a long day, lots of code writing.  But it was fun, because I was working on an interesting inverse problem.  Probably not that interesting to people who know lots about inverse theory, but it’s new to me, so still very cool.  Since I’m not great at writing efficient code, it was a long 6 hours before I could see any results.  But in the end I got a really pretty picture that might tell me something about using earthquake positioning techniques to locate a whale far outside a seismic network.  Well, about 15 km outside a network that covers roughly 5km x 10km of seafloor in 2km water depth.  So pretty far.

And yes.  I am a day behind in my little drawings.  At some point I will surely skip a day.  But I’m trying to keep up for as long as I can.

Oh… what’s that you say?  You want to see the results of yesterday’s work?  Alright!  It might not make sense, and there is always a chance it’s just outright incorrect.  But at the very least, those are some dramatic colors, no?  I had to scale the color values though – basically the colors are in a log scale.  So where it says 10, it actually means $10^{10}$, an 8 means $10^{8}$, and so on.  So yeah, those position errors way outside the network are huge.  HUGE.

## Lloyd’s mirror and BBQ chicken

Hey, here’s my drawing from yesterday. It was an inverse theory day. I think that the conference got me all fired up about inverse theory for some reason. It might not be the best idea ever to change my term project two weeks before the end of the term… but my other project is sort of boring.

I’m in the process of writing code to do a couple of things. The first is to locate a whale (or any source) in the water column using earthquake location techniques. I’m assuming that I correctly pick the direct path arrival. So that part should be easy. I’m running it several times on an array of grid points.  So for each point I get a cluster of detections, and then I grab the eigenvalues and eigenvectors to get the semi-major and semi-minor axes (with orientation) of the error ellipse.  As you can imagine, this takes a long time.  It’s an iterative least squares problem, being done like 6500 times * 50 iterations for each time.  And 50 is sort of low.  Hooray for the brute force method!  Here’s a little peak at just one of those iterations.  Because the whale is not in the network, the position is not great.  It’s really difficult to resolve the range, in particular, although the bearing seems better constrained.

The second bit of code I’m writing up is not actually finished yet.  Or started.  All I have is the math, which tends to be the tough part anyway.  The whale call arrives at our seismic network via several paths.  There is sometimes a direct path arrival, but often multipaths, which have interacted some number of times between the surface and the bottom.  The multipath structure will change depending on where the whale is, and theoretically, it is possible to back out at least a range and depth using the multipath arrival times.  Again, this is a problem that has been solved before.  But it’s fun to figure it out for myself.

Some other things I’ve been thinking of trying:

• Combine several range solutions from the multipath arrivals to locate the whale.  This shouldn’t be very hard.  It’s just like positioning a pinger on the bottom of Portsmouth Harbor!
• Implement some kind of adaptive tracking algorithm… I feel some Kalman filtering coming on…

## ASA and Thai food

Dax and I went to the ASA (Acoustical Society of America) meeting today.  It’s taking place down at the Sheraton, and the session we went to was upstairs in the Issaquah room (yes, I spelled Issaquah wrong in the little drawing).  The general topic was sound propagation and applications in bioacoustics, so a really interesting mix of talks.  It was cool to see what people are doing – lots of time-difference of arrival stuff (TDOA).  I was especially interested in how people deal with multipath arrivals, since that’s pretty much what our data is all about.  In fact, we often don’t even see direct path arrivals at all.

One of the talks that sparked my interest was by Xavier Mouy (although it was presented by one of his colleagues because he couldn’t make it to the meeting).   I’ve read one of his earlier papers on detecting fin and blue whales in the St. Lawrence.  His talk today was on locating walruses using the multipath structure on just one hydrophone.  Dax’s work is really similar in that he has done the multipath fitting using multiple receivers, along with ray tracing in complex bathymetry.

And tomorrow, we give our talks!  🙂

## Forearc basins and Greek yogurt

On Thursday we’ll have a full lecture on strongly non-linear inverse problems.  I’m just starting to warm up to the weakly non-linear inverse problems.  One big local minimum is good enough for me!  It was a tough class.  We went through our entire homework set from about a month ago where we did a series of linear algebra proofs.  It was tedious, but good to get an explanation of the underlying implications.  And I guess it was kind of neat to show that the solution found using singular value decomposition is identical to the solution found using eigenvalue decomposition.  🙂

## Earthquakes, tides, and tennis balls

A long day of writing code, taking partial derivatives, and walking Trooper.  That’s pretty much it.