Earthquake occurrences were generally indicative of Poisson distributions when considering a relatively low number of days (100 days) and got superseded by the negative binomial distribution due to the inflated presence of days with 0 events for larger periods (500 days).
This readme document will contain very brief description of some of the results that are fully available for perusal in this repository.
We examine, amongst a number of features, the time between earthquakes. This is done separately for earthquakes for earthquake ranges of 1 (eg 3-4, 4-5 etc). This is done because earthquake arrival times are a significant contender for a typical Poisson process for most studies. While this varies greatly for different scenarios, this was highly corroborated by the fact that the distribution of inter-arrival times strongly followed either an exponential or gamma distribution. This was significant becaues a feature of homogenous Poisson Processes is that the distribution of inter-arrival times follows an exponential distribution.
Let us have a quick look at a Cullen and Frey plot for inter-arrival times of Earthquakes for our 100 day sample (we did 100,250 and 500 day samples for this study)
Wonder what their distributions look like based off of magnitude? Here are some plots for 4-5,5-6 and 6-7 for this 100 day period for the GEONET catalog of recorded earthquakes!
Below is a facetted plot showing how the corresponding IRIS dataset (instead of GEONET's above) distributions' shapes change with different magnitude ranges.
Let us look at the same plots but for a 500 day catalog for both GEONET and IRIS!
A more nuanced or fine grained attempt at classifying based off of magnitude instead of our 1.0 magnitude ranges may be appropriate for a future experimentation.
Generally, it was determined that as opposed to an exponential distribution, inter-arrival times appear to fit the Gamma distribution better, at least for the GEONET datasets for both 100 and 500 day samples. It is arguable that aside from gamma, or a standardized beta distribution (which is not usually a practical application), the exponential distribution is the next best fit for the data. Notice that an 'IRIS' dataset was mentioned in this simple showcase. This repository in fact has the equivalent IRIS databases imported to compare with the GEONET databases for the same time periods for the reader's curiousity. The corresponding R files that conduct the analysis and Python file(watch.py) used to extract the information are available for you as well.
An interesting feature of exponential functions to take note of, is that the sum of various independent exponential variables, tends to lead to a Gamma distribution! Add to the fact that earthquakes, especially of higher magnitudes, cause aftershocks, which are smaller magnitude versions of the original earthquake originating from the same, adjacent or at least similar faulting structure.