2
$\begingroup$

What is the proper way to calculate cumuluative moment magnitude if I know the moment magnitude of several earthquakes?

$\endgroup$
  • $\begingroup$ I've no experience in calculating cumulative magnitudes, but if the question is just about how to add exponentials it would be: $log_{10}(10^{M_1}+10^{M_2} ... 10^{M_n})$. $\endgroup$ – Tactopoda May 20 '17 at 14:06
2
$\begingroup$

The moment magnitude ${\displaystyle M_{\mathrm {w} }}$ is a dimensionless number defined by Hiroo Kanamori as:

$$M_{\mathrm {w} }={\frac {2}{3}}\log _{10}(M_{0})-10.7$$

To sum several moment magnitudes we need to first convert them to ${\displaystyle M_{\mathrm {0} }}$ (seismic moment) which you can simply sum and then convert it back

  1. for each of the magnitudes you have - insert the magnitude into ${\displaystyle M_{\mathrm {w} }}$, solve for ${\displaystyle M_{\mathrm {0} }}$ and write down the answer.

  2. Sum all the answers

  3. Insert the sum back into ${\displaystyle M_{\mathrm {0} }}$ and solve for ${\displaystyle M_{\mathrm {w} }}$

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.