Our guest spot for this unit is professor John Rundle.
He is distinguished professor of physics and
geology at University of California, Davis.
He is also an external professor at the Santa Fe
Institute and he works on developing methods
for earthquake forecasting and risk management,
using dynamical systems and other complex systems
methods and extending those methods to other
natural phenomena, such as economic crises.
So welcome, John. Thank you. Our class is currently
covering fractals. We haven't talked about
power laws yet, but we've talked about fractal
dimension and we've looked at some famous fractals.
What would you say is relevant to fractals in your
own research? OK, so earthquake faults -
earthquakes are current earthquake faults and earthquake
faults are irregular objects and if you look at them geologically
in the crust you have faults of all scales,
all sizes and the individual faults themselves -
people have looked at the sort of fault trace,
if you will, and found that they seem to have
various fractal characteristics geometrically.
In addition to the geometrical object of the fault
is earthquake fault is the statistics are also
fractal in a sense in that they have power laws.
So if you look at the number of small earthquakes,
as a function of their what's called a seismic
moment, which is a measure of the energy put
out by the fault. That turns out to be a power
law. It reflects the fractal characteristics
of the underlying fault structure. OK. So the fun
way in which fractals enter into what we do.
OK. In the class we looked at a little bit of
fractal analysis of time series, like for stock prices
and we're wondering about how useful those kinds
of analysis techniques are in giving you insight
into what's going on say in earthquake time series.
There's been a lot of recent work by people like
Gene Stanley and Didier Sornette and some others
on the details of the analogy or metaphor if you will,
between earthquakes and financial crashes.
In fact, it's kind of interesting there have been
a number of recent books in the financial literature
where they talk about crashes as earthquake-like
events and the crashes often have what people
refer to as aftershock events. So it turns out
the statistics are very similar if you look at
the tails of the...if you look at price changes,
daily price changes
in the financial markets and you look at the
number of price changes as a function of their
size and you restrict yourself only to the biggest
price changes, it turns out that those statistics
look very very similar if not identical to the
statistics of large earthquakes. So the tails of
the distributions seem to be very similar and
there is the tendency to want to identify large
crashes with earthquake-like events.
So I've read that there's some kind of controversy
about applying statistics like fractal dimension
and related fractal characteristics to things like
stock prices and other phenomena. Do you think
that those are valid methods of analysis?
I do, because we actually looked at theses things
in a variety of different ways through a variety
of different sort of mathematical lenses and
we've actually concluded that there are useful
physics involved in this analogy. A lot of what
I'm doing recently is not so far been published,
because we've been looking at real financial
systems with these ideas and I'm consulting at
the moment with some hedge fund guys and actually
produce algorithms that are useful in trading
and it turns out so far these algorithms are
really quite useful.
In terms of earthquake
forecasting, what's the state of the art?
So in terms of earthquake forecasting, the basic
idea is this: We look at the Gutenburg-Richter
magnitude frequency relation. I didn't say
those words before, but that's essentially what I
was talking about when I said a number of small
earthquakes is large relative to the number of
big earthquakes. So it's power law. You can
understand it this way - for every thousand
magnitude three earthquakes there's approximately
one magnitude six earthquake. For every magnitude
four earthquake there's roughly ten magnitude
threes, a hundred magnitude two's and so forth.
So you can use this relationship in the following way:
If you look in a region where you've recently
had say a magnitude six earthquake and you just
start counting magnitude three's, then after you
counted another thousand magnitude three's it's
about time for another magnitude six. OK?
So this is the basis for the forecast that we
have embedded into a website called
openhazards.com. So you can go there and get a
global forecast. It's free and open to the
public, anywhere in the world, based upon this idea.
OK, and how successful has it been at forecasting?
We can test the forecast with the standard test
for forecasting, which are Brier skills scores,
reliability attributes tests, receiver operating
characteristics test. All these tests are used
for forecasting, for weather forecast as well
as financial forecast and you can actually construct
forecast to do pretty well. Now, with that being said,
we do deal with probability. One of the interesting
things that we've recently seen is if you look
in the Japan region, so if you look at all of Japan (the
region right around Japan) that was as people know
on March 11, 2011 there was a magnitude nine
earthquake there, which killed 20 000 people
with a tsunami. It turns out that since that magnitude
nine earthquake there had been about a thousand
magnitude fives. So in just the last two years
there had been a thousand magnitude fives.
Now this relationship that I told you about earlier
would seem to imply that for every thousand fives
there's a hundred sixes, ten sevens and one
magnitude eight is due. So this would seem to imply
that Japan right now is at risk for a major
earthquake of magnitude eight or larger. In the
relatively near future. The next year or two.
OK, so this is actually...we've actually put
this out on a blog on our website notified as
many people as I can think of about this possibility
and we'll see what happens. This relationship -
this Gutenburg-Richter magnitude frequency relation,
this power law statistic has indeed been seen
to be true in every region in the earth where
people have looked and for all times. So it
seems to be a fairly robust statistic.
But you can't really predict when the earthquake
is going to happen within a year or something,
can you? Not at the present time. We can only say
that the conditions are in place for such a major
earthquake in the relatively near future.
OK, do you think the same kinds of methods will
apply to predicting crashes and financial markets?
Very good question. I don't know the answer
to that yet, because we haven't really looked
in that direction yet, but as you know and maybe
some of the people on the course know the statistics
of price changes are what they call lepto cryptotic
so it's got power law tails and it looks something
like a Gaussian in the middle, so it's a little
bit different than earthquake faults, which
looked to be pretty much pure power law.
The ideas should translate in some way and we
haven't really looked at that yet, but we will.
So what's the most exciting thing you 're working
on right now, exciting to you. Right now we're
still working on the earthquake forecast and
we're also working on numerical simulations
of massive fault models, earthquake fault models.
These are models in which - they're rather like
climate models so we build systems in the computer
that have many faults and sub-faults and pieces
of faults and let them interact and they have friction
on them. The idea is to generate a synthetic
time histories of millions of earthquakes and
study the statistics of those.
Great and my very last question is: We have
a lot of people on this course in different
fields and some of them are interested in getting
into complex systems, but are daunted by the
number of different areas that one needs to know,
So can you say a little about your advice to students
who were interested in getting into the field
of complex systems? Advice to students getting
into complex systems? Well, the thing I would say,
two things, several things is one is you need to
have a pretty good computational background.
You need to have some knowledge of mathematics.
But not an extraordinarily high level of knowledge
you certainly need to know calculus, you definitely
need to know something about probability and
statistics and you need to have an open mind.
You need to consider lots of different ideas
and the fact that systems, which appear to be
quite different may in fact be in some underlying
way very similar. That is a very big leap of
imagination for some people and some professionals
who devoted their lives to a particular field,
but it's a leap you need to be able to make
in order to make any progress in this field.
Great, well thank you so much.
OK, thanks.