Propagating Waves

A devastating earthquake, 8.9 on the Richter scale, hit Japan today, causing extensive damage and a large tsunami. I can’t imagine what it would be like to look out your window and see something like this headed your way. Our thoughts go out to everyone affected by the disaster.

A force this big propagates around the world, so beaches here in Southern California were expecting heightened wave activity — nothing very serious, but certainly noticeable. Scientists of course immediately leapt into action to estimate what kind of effects should be expected. The National Weather Service circulated this map of predicted wave heights. Click to embiggen.

Naturally, the House of Representatives is trying to cut funding for tsunami warning centers.

37 Comments

37 thoughts on “Propagating Waves”

  1. Does the falloff of amplitude with distance approximate a 1/r law since they’re propagating in 2 dimensions?

  2. apikores: The energy flux of a wave is proportional to its amplitude squared. In 2D, the energy flux should indeed vary as 1/r, so the amplitude should vary as 1/sqrt(r).

    I was looking at the curved red band running from Japan to Chile, and was wondering if its shape was governed by the Coriolis force (veering to the right in northern hemisphere, and then to the left after it has crossed into the southern hemisphere).

  3. Wouldn’t the depth/shape of the seafloor also vary the “index of refraction” the wave is travelling through?

    Also, something I haven’t heard anything about is the effect if any of the earthquake and tsunami on sea life. Would the underwater acoustics of a large earthquake injure nearby sea life? Farther out I’d assume a wave in deep ocean wouldn’t have much effect, but I could imagine it could do some damage in shallow water near land if the current tore up the sea floor.

  4. @dbh: Coriolis might enter into it somewhere, but I’d guess that most of the curve is an artifact of the rectangular projection of the globe’s surface. Great circles that don’t follow a line of latitude or longitude are mapped to curves. You may have noticed similar curves when looking at NASA diagrams of the position and trajectory of the ISS and other satellites of interest relative to the ground below.

  5. Zombie: The most obvious victims from the marine life would be the washed ashore fish, turtles and deeps sea creatures. Apart from that the corals are often buried in the sand moved by the currents. Also I’ve heard about fossils preserved in the so called ‘tsunami beds’.

    How does the speed of propagation vary with the distance from the epicentre? What about the speeds of the underwater current from the epicentre onward?

  6. What would Coriolis force have to do with it? What is being transported is the disturbance, not water.

  7. mah? dbh? Those trajectory curves you see on this map and satellite trajectory displays come about from those map’s projections of great-circle plots and have nothing whatsoever to do with Coriolis. DUH.

  8. Just a small correction. Shouldn’t the beginning say 8.9 magnitude and not Richter scale. Moment magnitude is now the scale that is used to measure the size of the earthquake.

  9. As a science geek I love this blog, it’s on my RSS reader and I check it out every day. But I wish you’d (used collectively, for all authors who contribute) all stick to science commentary. Whenever you write posts or little blurbs relating to politics/public policy, it turns me off.

    A little while ago this blog had a post about ‘anti-science’ Republicans because they’re talking about cutting government funding. That post was bad enough, but this one is a hell of a lot worse. The GOP won a landslide in last year’s elections primarily because of their fiscal stance – the US is spending too much money (on everything!) and they promised cuts. But now you, and Think Progress (a partisan liberal organization/website) are insinuating, if not stating it outright, that defunding this activity would kill people.

    NOAA is a multi-billion dollar government agency with wide-ranging activities – not just tsunami warning centers. In a deep recession, where the private sector has had to make sacrifices to remain fiscally solvent, NOAA’s budget has increased. You won’t find that on the Think Progress link you provided, but a quick Google search will send you to NOAA’s own FY11 budget highlight .pdf file. Their FY 08 budget was $3.8 billion, their FY09 budget was $4.3 billion, their FY10 budget was $4.7 billion, and they’ve requested $5.6 billion for FY11 (a year for which there is no budget).

    In Washington double-speak, a decrease in the amount an agency is expected to increase year over year is called a ‘cut.’ So while funding may have actually increased, people will scream that it was ‘cut’ because it didn’t grow as much as projected. I think that’s what has happened here (although I can’t be 100% sure, and don’t have time this morning to do that level of research).

    It’s funny, when this blog talks about science, you are very clear about what you know and what you don’t know about a subject, dark matter for example.

    But when the subject turns – however briefly – to public policy, the liberal talking points come out with no qualifications, no exploration of contrary views, and no explanation about what you’re doing.

    What concerns me is people who give deference to your thoughts on cosmology will give similar deference to your thoughts on public policy, an area where you’re out of your depth.

    As I said, I enjoy this blog for the science. I wish you’d stick to that.

  10. Anonymous_Snowboarder

    Sigh.. Did you even research the numbers? Or did you just look for the most biased reporting you could find? First off, there is no line item in the budget which I can find (Obama’s or the House) specific to tsunami warnings. So any reductions in funding to NOAA are up to NOAA to allocate. Second, in 2009 (actual, per Obama budget doc) NOAA had $3.13B and $1.24B for Operations,Research,Facilities and Procurement respectively. The 2010 estimate was $3.41 and $1.36 and Obama’s 2011 proposal was $3.41B and 2.18B. What was the House bill? $2.85B and $1.46B.

    So basically you (and other progressives) are arguing that NOAA can’t possibly make it on 2009 funding levels (the House proposal)? I second what Tom W says – we all enjoy the science content of the blog and while it is certainly your perogative to include politics please at least try to keep that discourse at the same level you would in regards to reporting on scientific observations and theories.

  11. One more thing, because this post has been bugging me all day.

    Of all the things you could have written – the magnitude of the tragedy, the science of earthquakes, to the science behind why more people didn’t perish in the quake – you chose to take a political shot at the House of Representatives.

    That, I think, says more about the author than it does about the House.

    You can, and should, do much, much better.

  12. Tom W and Anonymous_Snowboarder: fair enough that a science blog should keep political posts separate from scientific ones. The last line muddled observation and analysis a bit.

    However, Discover does have a responsibility to advocate for research, especially in cases like Japan’s wherein research’s importance to society is so plain. (And I don’t want to press on about politics, but it’s worth mentioning the folly of the government cutting funding because “the private sector has had to make sacrifices to remain fiscally solvent” – Who, precisely, is supposed to be doing the spending these days? And since when does 4.37 equal 4.31? And what’s $60 million between friends?)

  13. Pingback: Reverberations | Cosmic Variance | Discover Magazine

  14. John H: Fair enough that Discover chooses to advocate for research, and I don’t dispute the importance of this research.

    However, ‘advocacy’ in public policy debates is non-scientific almost by definition. Scientists seek truth, and as there is no ‘truth’ in politics. Once you blur the lines between the two you get in trouble, fast.

    So if Discover wishes to advocate for research, I would suggest they state it early and often. Perhaps they have and I’ve missed in, in which case I apologize in advance.

    And as long as you’re not pressing on about politics (apparently putting it in parenthesis isn’t pressing on), it’s striking how many people interested in science choose not to apply those skills when debating economics or public policy. Ask Greece if it’s folly to continue to grow goverment spending in the midst of a deep recession.

  15. Ask Greece if it’s folly to continue to grow goverment spending in the midst of a deep recession.

    Greece’s problem is that they don’t control their own monetary policy.

    The US does. That’s the difference.

    (Greece has other problems, which the US does not, but that’s the central one at issue here.)

    And, no, ” grow[ing] goverment spending in the midst of a deep recession” is not “folly”. It’s standard macroeconomic wisdom, since … well, since the Great Depression taught us the folly of doing otherwise.

  16. Jacques – your post, as well as your blog, is a perfect example of what I’m talking about when I say there is no ‘truth’ in public policy.

    Consider this science example – dark matter vs. MOND. Each has their proponents, and each has data that support their conclusions/predictions. But only one side is right, we just don’t yet know for sure which one (although the balance of opinion is on one side).

    Public policy has the same features – except absolute truth. There is no ‘right’ way to govern a population of people. But lots of people, and in particular very well educated people, like to think that truth exists and their side has a monopoly on that truth.

    There is a post on your blog talking about the deficit and its conclusion is the Bush-era tax cuts are responsible. Lots of nice facts and data to support your conclusions, it is very well done. Only one problem – you don’t discuss the spending side of the equation. One could also argue, as many have, that steep spending increases are to blame for the deficit and back it up with all sorts of data. That argument would be equally as correct as your argument.

    The difference is personal preferences. I, personally, prefer to live in a society governed by a small, limited government. I infer, based on your writings, that you prefer a much larger, more activist government. Are either of us ‘right’? No, but we each have to make the case to our fellow citizens and try to convince them to follow us.

    Which brings me back to your comment, where you make two declarative statements purporting to be of fact: Greece’s central problem is they don’t control their monetary policy, and growing government spending in a recession is standard macroeconomic wisdom from the Great Depression. However, those are both statements which originate from a more liberal political view of economics and public policy. One could easily say, and be equally right, that Greece’s central problem is too much spending. And if you’ve figured out the Great Depression you should be on Wall Street, not in Austin, because its causes and implications have been the subject of much study and debate.

    It feels like I’ve hi-jacked this thread, and it wasn’t my intention, but my point remains the same. Science and public policy advocacy don’t mix, and just because someone has an extensive background in and knowledge of, for example, physics, doesn’t mean s/he is equally well versed in public policy. And on a science blog, unless the author states his party/preference/position up front, the two shouldn’t mix.

  17. One could also argue, as many have, that steep spending increases are to blame for the deficit and back it up with all sorts of data.

    One could argue that, but one would have a hard time backing it up with actual data.

    Spending (even including the TARP and the Stimulus package, which both produced temporary upward blips) has tracked its pre-recession trend. Revenues fell off a cliff, and have not recovered. That is the source of our current, large deficits.

    Yes, you are entitled to your own set of preferences for the optimal size of Government. You are not, however, entitled to your own set of facts.

    I agree that we have drifted off-topic.

  18. Jacques – from the portions of your blog that I’ve read, I understand you to be an intelligent man. Having said that, you appear to be misunderstanding my entire point. Politics is about preferences. Your link leads the reader to Krugman’s blog. He is a Nobel Prize winning economist. More importantly, however, to our current discussion is the fact that he is a partisan liberal. You throw out a Krugman citation and I can throw a Friedman citation right back at you. Or, if you’d prefer a more timely and thorough analysis, Google this: USA, Inc (http://www.kpcb.com/usainc/USA_Inc.pdf). It’s roughly 46o slides worth of analysis on the US’s current fiscal stance. Interesting reading no matter what side of the political isle you find yourself. And it comprehensively analyzes the spending increases (think entitlements!) that have us in our current predicament.

    And as you’re an intelligent man, I shouldn’t have to explain the fallacy in your argument. Yes revenues have fallen off due to the recession (and also, arguably, the Bush tax cuts, although depending on your opinion of where we are on the Laffer curve, tax cuts can actually increase government revenue) – but during that time spending has increased! Say, for example, you are forced to take a pay cut at work and at the same time decide to buy a new SUV which, by the way, you couldn’t have afforded if you still had your older, higher salary. By your logic, your household deficit is caused by the pay cut, not the decision to buy a new vehicle, when clearly both forces are at play.

    There are two sides to a balance sheet – that was the rather simple, pedantic argument I attempted to make. But you couldn’t let that one go! And my point was not to say that you’re wrong, although I certainly do think so. My point was that in almost every public policy debate, there are two VALID sides to an issue, and neither one is necessarily right.

    If your preference is, as I suspect, a large activist government, then say it proudly! But please don’t accuse me of inventing or ignoring facts when in fact it’s policy preferences that separate us.

    And I think, if nothing else, that this whole discussion has illustrated why science blogs should, in almost all circumstances, shy away from public policy.

  19. You throw out a Krugman citation and I can throw a Friedman citation right back at you.

    Not if what you said about the Great Depression is any guide. Milton Friedman understood the causes of the Great Depression.

    Uncle Milton would call you nuts for advocating spending cutbacks in the middle of a recession.

    Yes revenues have fallen off due to the recession (and also, arguably, the Bush tax cuts, although depending on your opinion of where we are on the Laffer curve, tax cuts can actually increase government revenue)

    “Which side of the Laffer curve” we are on, is not (or should not be) a function of one’s ideological persuasion. To assert that it is, is the sort of thing that really ticks me off. Sorry, but I’m funny that way…

    My point was that in almost every public policy debate, there are two VALID sides to an issue, and neither one is necessarily right.

    In any public policy debate, there are, inevitably, multiple sides to an issue. What we should do about a given set of facts is a matter on which reasonable people may disagree.

    Disagreeing about what the facts are, is quite a different matter.

    “[S]teep spending increases” is a factual statement about the rate of change of government expenditures. It is a statement that can be compared with actual rate of change of government expenditures. That’s what the graph on Krugman’s blog (not his graph, the St Louis Fed’s graph) does. You may decide that you don’t want to look at the graph, because Krugman is a liberal, but that doesn’t actually affect the rate of change of government expenditures over recent years.

    And it comprehensively analyzes the spending increases (think entitlements!) that have us in our current predicament.

    “Entitlements” is much too vague a term. There is one threat to our long-term budgetary outlook, that makes everything else irrelevant: Medicare.

    Fix Medicare’s cost growth, and you’ve fixed the long-term budgetary crunch. Don’t fix it, and nothing else you do makes any difference.

    I recommend reading carefully the Medicare section of that USA-Inc pdf that you linked-to. The rest of it is irrelevant fluff.

    In any case, that has absolutely nothing to do with current deficits, or the proper response to the Great Recession.

    Say, for example, you are forced to take a pay cut at work and at the same time decide to buy a new SUV … By your logic, your household deficit is caused by the pay cut, not the decision to buy a new vehicle, when clearly both forces are at play.

    Say I had previously accumulated a healthy nest-egg. Would my SUV purchase still be immoral (since your argument seems to be a moral, rather than a financial one)?

    Perhaps I squandered that nest-egg by buying rounds for my drinking buddies. But, say my local bank were willing to loan me the money to purchase the SUV at, say, 2%/yr for a 5-year term — an interest rate well below what anyone else in the neighbourhood can get? Would it still be immoral for me to purchase the SUV?

    Or, more personally, do you own a home? If so, your mortgage is probably many times your annual net income. And, yet, you’re not worried. Why is that?

  20. Just in case anyone didn’t know by now, the earthquake was retroactively upgrade to a M9.0 on the richter scale. I’m still feeling the aftershocks today. There was one half an hour ago.

  21. Jacques – this debate is interesting to me because I think it illustrates a point I made in my response to your first comment. I may be mischaracterizing your views a bit, but you seem to think there is ‘truth’ in public policy and yours views more closely match that truth than do those on the other side of the isle. You use what purport to be statements of fact (“has absolutely nothing to do with out current deficits”) that are fact statements that reflect policy preferences. I can’t decide whether or not it’s purposeful, but I’ll give you the benefit of the doubt and assume bias is clouding your thinking.

    For example, you seem to indicate that my use of the term ‘steep spending increases’ isn’t factual. I will stipulate that ‘steep’ is subjective and a matter of opinion. ‘Spending increases’ is a factual statement and one you do not dispute, apparently. Also note that I referred in that sentence to the debt, not the deficit, two different but related things.

    The rest of your discussion of that subject is based on policy preferences – you think TARP and the stimulus was a good idea and have a theory and data to back it up. A perfectly reasonable position. Others think that they were a bad idea, and have a theory and data to back that up. Another perfectly reasonable position. Economics in particular and public policy in general are not fields where, like the hard sciences, hypothesis can be falsified by experiment and exact forcasts can be made about future outcomes.

    Is democracy preferable to communism? Most Americans would say yes, but it’s not a question that can be answered scientifically. Was the stimulus preferable to inaction? We won’t ever know, but Obama had an economic team od advisors forecasting all kinds of great benefits that never came to pass. They had predictions based on calculations and models derived from their own viewpoint/theories/biases. Again this is perfectly reasonable.

    But what you fail to do is give any credence to is the reasonableness of arguments from the other side. My last comment implored you to admit that a deficit has two components, spending and revenue. You not only wouldn’t do that, you went on an irrelevant tangent about driking buddies and terms of a car loan. I also asked you to state outright what your policy preferences were with respect to the size and activity level of the federal government, and you chose not to.

    If we cant at least agree to argue from a common starting point, using common language, then we have no place left to go.

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