<p>I need a (rough) functional relationship between these three quantities. My initial hypothesis is that the risk <span class="math-container">$R$</span> (intended as the probability of a building damage), scales with the square root of the distance <span class="math-container">$r$</span> and increases exponentially with the magnitude <span class="math-container">$M$</span>, but I am not sure about the correct normalization <span class="math-container">$k$</span>.
<span class="math-container">$$R(r,M) \simeq k\frac{10^M}{r^2}$$</span></p>
<p>I need this to estimate the potential damage of an earthquake on physical infrastractures.</p>

CC BY-SA 4.0
2023-03-12T23:58:06.347Z
Perhaps you should explain why you need this??  It sounds like something you could get some data and tend to determine covariances for yourself if interested?
JeopardyTempest
CC BY-SA 4.0
2023-03-13T08:49:21.147Z
I need this to estimate the potential damage of an earthquake on physical infrastractures. Which data should I use to make the fit that you are suggesting?
AbateFaria
CC BY-SA 4.0
2023-03-13T11:42:09.243Z
As currently written, the question is not specific enough. The word risk has many meanings to different people. I'm assuming you mean risk of property or building damage. What about collapse of the land surface & land displacement? The recent earthquake in Turkey caused parts or the land surface to collapse leaving very deep & wide gullies, ruining once productive olive groves. One factor which you omit is depth of the quake source. Earth vibrations near a shallow high magnitude quake will produce catastrophic effects, whereas a deep quake of low magnitude will negligible far away.
Fred
CC BY-SA 4.0
2023-03-13T16:03:23.630Z
Yes, for risk I mean the probability of a building damage. I wonder if are there some "standardized" measures of this kind. Regarding the depth of the quake source, maybe it can be inserted in my formula just by considering $r$ as the distance from the source event, instead from the epicenter.
AbateFaria
CC BY-SA 4.0
2023-03-13T22:29:08.990Z
Damage is not just a function of distance. It is very much a function of local geology too. People create what are called "ShakeMaps" for specific areas to highlight this relationship. Take a look at the picture here, for example: https://en.wikipedia.org/wiki/Strong_ground_motion If you look closely, the predicted ground motion is not just a function of distance.
Wolfgang Bangerth
CC BY-SA 4.0
2023-03-14T03:29:14.200Z
Not to pile on, but I'd think the danger of building damage is extremely dependent on construction technique too.  Or as a limited proxy, could perhaps use something like GDP that likely has some correlation to technique.
JeopardyTempest
<geophysics><earthquakes><seismology><mathematics>
What is the relationship between earthquake risk, magnitude, and distance from the epicenter?
AbateFaria
# What is the relationship between earthquake risk, magnitude, and distance from the epicenter?

(Asked by: username_0 on 2023-03-12)

I need a (rough) functional relationship between these three quantities. My initial hypothesis is that the risk $R$ (intended as the probability of a building damage), scales with the square root of the distance $r$ and increases exponentially with the magnitude $M$, but I am not sure about the correct normalization $k$.
$$R(r,M) \simeq k\frac{10^M}{r^2}$$

I need this to estimate the potential damage of an earthquake on physical infrastractures.

**Tags:** geophysics, earthquakes, seismology, mathematics

> **Comments:**
> **username_1**: Perhaps you should explain why you need this??  It sounds like something you could get some data and tend to determine covariances for yourself if interested?  
> **username_0**: I need this to estimate the potential damage of an earthquake on physical infrastractures. Which data should I use to make the fit that you are suggesting?  
> **username_2**: As currently written, the question is not specific enough. The word risk has many meanings to different people. I'm assuming you mean risk of property or building damage. What about collapse of the land surface & land displacement? The recent earthquake in Turkey caused parts or the land surface to collapse leaving very deep & wide gullies, ruining once productive olive groves. One factor which you omit is depth of the quake source. Earth vibrations near a shallow high magnitude quake will produce catastrophic effects, whereas a deep quake of low magnitude will negligible far away.  
> **username_0**: Yes, for risk I mean the probability of a building damage. I wonder if are there some "standardized" measures of this kind. Regarding the depth of the quake source, maybe it can be inserted in my formula just by considering $r$ as the distance from the source event, instead from the epicenter.  
> **username_3**: Damage is not just a function of distance. It is very much a function of local geology too. People create what are called "ShakeMaps" for specific areas to highlight this relationship. Take a look at the picture here, for example: https://en.wikipedia.org/wiki/Strong_ground_motion If you look closely, the predicted ground motion is not just a function of distance.  
> **username_1**: Not to pile on, but I'd think the danger of building damage is extremely dependent on construction technique too.  Or as a limited proxy, could perhaps use something like GDP that likely has some correlation to technique.  

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## 0 answers

