In this paper, we investigate questions arising in Parsons & Geist (2012). Pseudo causal models connecting magnitudes and waiting times are consider, through generalized regression. We do use conditional model (magnitude given previous waiting time, and conversely) as an extension to joint distribution model described in Nikoloulopoulos & Karlis (2008). On the one hand, we fit a Pareto distribution for earthquake magnitudes, where the tail index is a function of waiting time following previous earthquake; on the other hand, waiting times are modeled using a Gamma or a Weibull distribution, where parameters are function of the magnitude of the previous earthquake. We use those two models, alternatively, to generate the dynamics of earthquake occurrence, and to estimate the probability of occurrence of several earthquakes within a year, or a decade.

5 thoughts on “Earthquake dynamics”

Very nice paper!
I was trying to reproduce with R what you did in your paper but I am struggling with a few things.
The very first one is that my plot of the Tail Index of the pareto distribution versus the Treshold of the Pareto distribution (magnitude) shows a decreasing curve from 3.5 to 0.2 (very far from the 1/2 you mentionned). Would it be because I took a too large area for my earthquakes?
My second question is how did you regress beta (depending on waiting times) in the Pareto Generalized linear model? How did you compute your Beta(d)?

Thank you very much for your help and for your blog which is one of the websites I go almost every day!

Great paper! Another nice contribution for a great blog on R and econometrics.

I was wondering whether you would want to share the R code for plotting figures 1 and 14? W.r.t. the former, the figure-in-figure is a nice touch; as to the latter, I am curious to know how you translated distance in km to the size parameters of the graph (par(“usr”)) for plotting the corresponding concentric circles (and the arrow indicating the radius) on top of your map.

thanks ! sure, I can do that, just give me a couple of days. But I should probably mention that I might not be using the best map projection to use circles as equidistant points… I will try to add some code to get the true graph !

Thanks. The dataset we use is a standard open dataset, available from http://earthquake.usgs.gov/earthquakes/search/. Then, all the details are mentioned in the paper (several restrictions were considered)

Very nice paper!

I was trying to reproduce with R what you did in your paper but I am struggling with a few things.

The very first one is that my plot of the Tail Index of the pareto distribution versus the Treshold of the Pareto distribution (magnitude) shows a decreasing curve from 3.5 to 0.2 (very far from the 1/2 you mentionned). Would it be because I took a too large area for my earthquakes?

My second question is how did you regress beta (depending on waiting times) in the Pareto Generalized linear model? How did you compute your Beta(d)?

Thank you very much for your help and for your blog which is one of the websites I go almost every day!

Benjamin

Great paper! Another nice contribution for a great blog on R and econometrics.

I was wondering whether you would want to share the R code for plotting figures 1 and 14? W.r.t. the former, the figure-in-figure is a nice touch; as to the latter, I am curious to know how you translated distance in km to the size parameters of the graph (par(“usr”)) for plotting the corresponding concentric circles (and the arrow indicating the radius) on top of your map.

thanks ! sure, I can do that, just give me a couple of days. But I should probably mention that I might not be using the best map projection to use circles as equidistant points… I will try to add some code to get the true graph !

Very interesting topic! Could you share your data?

Thanks. The dataset we use is a standard open dataset, available from http://earthquake.usgs.gov/earthquakes/search/. Then, all the details are mentioned in the paper (several restrictions were considered)