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# [SEAOC] Re: [SEAOC] Help: Calculate Ms from Ml or Io ...

• To: seaoc(--nospam--at)power.net
• Subject: [SEAOC] Re: [SEAOC] Help: Calculate Ms from Ml or Io ...
• From: jacob(--nospam--at)ldgo.columbia.edu (Klaus Jacob)
• Date: Thu, 23 May 96 10:01:14 EDT

```In response to :

>Does someone know of a formula to calculate:
>
>1. Surface wave magnitude, Ms, from a given epicentral distance, Io (MMS)
>   (...and vice versa)?
>2. Surface wave magnitude, Ms, from a given local magnitude, Ml (Richter)
>   (...and vice versa)?

>Peter Rangelow
>====================================================================
>Deutschherrnufer 29       tel  : + (49-69) 621-720
>60594 Frankfurt am Main   fax  : + (49-69) 621-720
>GERMANY                   email: rangelow(--nospam--at)mail.pop-frankfurt.com
>====================================================================

As one of the other responders to your question pointed out, this is a
region-specific issue for the following reasons: Maximum intensity Io,
surface-wave magnitude Ms, and local Richter magnitude Ml are measuring
different portions of the spectrum, and therefore when different regions
produce spectrally differently colored ground motions you get different
relations between the above quantities.

The moment magnitude Mw, not mentioned by you, is currently the preferred
magnitude based on the long-period end of the spectrum and is least
affected by regional source ( i.e. stress-drop, depth, thrust vs.
strike-slip etc.) or wave propagation differences (crustal velocity
structure and attenuation, 1/Q, etc.). In short all these regionally
differing physical properties require regionalized relations of the sort
you are asking for. Most relations are pretty uncertain and often apply
only to certain distance and magnitude ranges. Given all these caveats,
here are a few examples that you may use as ball-park indicators:

For example for
NW Europe, Ambraseys (1985a) gives:       Ms=0.09+0.93Ml
W. Africa, Ambraseys and Adams (1986b):  Ms=0.40+0.76Ml

and as a very crude relation between body wave magnitude mb (that is not
too different in most regions from Ml)  Nuttli and Herrmann (1979) get for
the central US:
Io = 2mb - 3.5
The most thorough compilation on this subject has been done by A. Johnston
for the EPRI global study of the seismicity of stable continental regions.

This is a business where you have to learn to take things with a grain of salt.

Viel Gluck !!
Klaus H. Jacob,  Ph.D.
Senior Research Scientist
Lamont-Doherty Earth Observatory (LDEO) of Columbia University
Route 9W, Palisades NY 10964, USA
Phone: (914) 365 8440;     Fax: (914) 365 8150

...

```