Analysis of frequency of earthquakes in Tarim basin, western China .

The selection criteria used to obtain the data from the USGS website on earthquakes was all earthquakes within a 700 km radius of a point at 90 longitude and 40 degrees latitude, which is centered just a bit north of the Tibetan plateau.

After computing the number of earthquakes > certain size seen per year in the 27 years of record the plots below were generated in Excel. The steps were to first rank the earthquakes by sorting in descending order and assigning an associated rank value in the next column. Then dividing the rank by 27 gives the number of earthquakes that size or larger per year. Considering the area, then this gives the number of earthquakes per year for that area, sort of a frequency density. The log was taken of this yearly frequency, and plotted as y against earthquake magnitude (which is already a log scale) as x. All the data yielded the plot to the left. An r-squared value of .91 suggests a decent, although not great, fit.

It is fairly common in these plots to see a curve at the lower magnitude end of the scatter plot, as you do here. This is a resolution screen operating on the data. Earthquakes in a certain size range can not be consistently measured by the seismic network, and below that they are invisible to the seismic network. By looking at the data one can estimate that below a magnitude 4 the network is not detecting all earthquakes in the region. If we eliminate those earthquakes we get a more useful linear regression with a higher correlation coefficient (r-squared=.96). Notice, however, that we must have good reason for removing our data from the analysis, and that we must make it clear that it was omitted. A careful look may suggest that we have not quite removed all of it.

While there is a good fit, note that at the very stretch of greater interest, that of larger earthquakes, we see the largest deviations from the line, and it is in a consistent manner. Considering the scale and extrapolating one might estimate a Richeter magnitude 8 earthquake should occur every hundred years or so. This is somewhat consistent with the tectonic setting. Note that this analysis does not speak to the scale limits on the fractal distribution of earthquakes. Put another way, we haven't addressed the important questions, what is the largest earthquake possible or likely in this area. More analysis and caution is needed if one wanted to speculate on the chances of a larger earthquake, but this shows a way to start. For estimating the frequency of moderate size earthquakes in the area this relationship would be far more dependable.