Verifying the Gutenberg-Richter law at small magnitudes

[Phyisab****]

So, I downloaded some earthquake data from the USGS database. I then plotted the log of the number of earthquakes with magnitude greater than or equal to M versus the magnitude M. This should produce a nice linear trend as predicted by the Gutenberg-Richter law. However, there is an apparent dearth of earthquakes at low magnitude.

Is this due to the sensitivity of instruments used to detect the earthquakes? Is this a well known occurrence? Is it affected by "declustering" of earthquakes at higher magnitudes?

 

[Phyisab****]

Anybody? Really?

 

[billiards]

Small earthquakes harder to detect, not really due to sensitivity of instruments, more to do with signal drowned in noise.

 

[G037H3]

Seems like you don't have a full data set. I also agree with billiards.

 

[LudusRex]

Thank you for sharing your findings on verifying the Gutenberg-Richter law. Your approach of plotting the log of the number of earthquakes versus magnitude is a common method used to confirm this law. As you have observed, there is a decrease in the number of earthquakes at lower magnitudes, which is a well-known occurrence in earthquake data.

The apparent dearth of earthquakes at low magnitudes can be attributed to the sensitivity of the instruments used to detect them. Earthquake detection systems have a minimum threshold for detecting seismic activity, and this threshold is typically higher for smaller magnitude earthquakes. Therefore, it is not uncommon to see a decrease in the number of earthquakes at lower magnitudes in earthquake data.

Additionally, declustering of earthquakes at higher magnitudes can also impact the data at lower magnitudes. This is because declustering removes aftershocks from the data, which are often smaller magnitude earthquakes that occur after a larger earthquake. This can result in a decrease in the overall number of earthquakes at lower magnitudes.

In conclusion, the apparent dearth of earthquakes at low magnitudes in your data is a common occurrence and is likely due to the sensitivity of earthquake detection instruments and the declustering of data at higher magnitudes. These factors should be taken into consideration when verifying the Gutenberg-Richter law at small magnitudes.