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

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

<p>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</p>

<ol>
<li><p>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.</p></li>
<li><p>Sum all the answers</p></li>
<li><p>Insert the sum back into ${\displaystyle M_{\mathrm {0} }}$ and solve for ${\displaystyle M_{\mathrm {w} }}$</p></li>
</ol>

CC BY-SA 3.0
2017-05-22T17:52:22.693Z
2017-05-22T17:52:22.693Z
OMRY VOLK
<p>What is the proper way to calculate cumuluative moment magnitude if I know the moment magnitude of several earthquakes?</p>

CC BY-SA 3.0
2017-05-20T14:06:19.550Z
I've no experience in calculating cumulative magnitudes, but if the question is just about how to add exponentials it would be: $log_{10}(10^{M_1}+10^{M_2} ... 10^{M_n})$.
user2821
<geophysics><seismology><earthquakes>
How to calculate cumulative moment magnitude?
ye-ti-800
# How to calculate cumulative moment magnitude?

(Asked by: username_0 on 2017-05-19)

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

**Tags:** geophysics, seismology, earthquakes

> **Comments:**
> **username_1**: I've no experience in calculating cumulative magnitudes, but if the question is just about how to add exponentials it would be: $log_{10}(10^{M_1}+10^{M_2} ... 10^{M_n})$.  

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## 1 answers

### Answer by username_2 on 2017-05-22. Score: 2 | Accepted answer

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 ${\displaystyle M\_{\mathrm {w} }}$


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