# Talk:Moment magnitude scale

## Notation

Why is moment magnitude indicated with the letters MW? What does the W stand for? -- Rod Thompson, Hilo, Hawaii

Good question... I don't immediately find the answer by googling. The notation was probably introduced in Kanamori's 1977 paper in the Journal of Geophysical Research, but I don't have that handy. The origin of notation in the sciences is often rather obscure. Gwimpey 06:14, 24 May 2004
In the equation for seismic moment is a capital omega not, which is equal to spectral amplitude at low frequencies and or equivalently on a broadband displacement seismogram the product of pulse with and amplitude. The lower case symbol for omega closely resembles a w. This was taken from an informal poll of workers that came in on a holiday at a large seismic network. Ref is "An introduction to the theory of seismology" by Bullen and Bolt page 426 and 427. (not my favorite seis book though) Annonymous
Interesting. So should we actually write MΩ or Mω? I know that some Microsoft programs convert "ω" into "w" and equivalently "Ω" into "W" when converting from Unicode to a non-Greek 8-bit legacy character set (which makes for interesting reading when having a "4.7 MW resistor" specified in a small circuit :-). In signal processing and physics (see ISO 31-2), ω = 2πf stands for the angular velocity, a measure of frequency that saves you having to write 2π in many formulas related to the Fourier transform. Is that what is used here, i.e. is the quantity meant to be frequency dependent? Markus Kuhn 11:22, 13 Jun 2005 (UTC)
The underlying question is, whether we should copy this rather confusing mix of indices on the magnitude quantity at all, or look instead for an existing more streamlined and systematic presentation and notation in the literature (a good textbook, some formal standard?) and take the notation from there, rather than from the original articles. Looking for some good books worldwide is probably more helpful than googling here. Any suggestions? Markus Kuhn 11:22, 13 Jun 2005 (UTC)
W stands for the "difference in elastic strain energy W before and after an earthquake" in : Kanamori H. (1977). The energy release in great earthquakes. J. Geophys. Res., 82, 2981-2987. This article is the reference paper for moment magnitude where it is defined for the first time. The original formulation links the energy called W in the paper to a new magnitude called by the author Mw. The relation linking the seismic moment to this magnitude, even if it is nowadays a common formula in seismology, is a secondary product in this article. The author gives only the relation between energy W and seismic moment M0. Thus even if deducing the formula between the seismic moment and the new magnitude is straightforward, the relation is not explicitly written. It is explicitly written (equation 4) in this brief paper : Hanks T. and H. Kanamori (1979). A moment magnitude scale. J. Geophys. Res., 84, 2348-2350. andre 09:57, 14 September 2006 (UTC)
To increase the likelihood of confusion with mega watts! Mu2 01:35, 27 May 2011 (UTC)

## More prominent: SI or CGS?

Shouldn't SI be more prominent? Do we even need the formula in CGS units? This unnecessarily complicates things. Shameer 01:14, 28 Dec 2004 (UTC)

Presumably, if developed in 1977, the scale may have been developed for cgs units. I'm not certain, but yes, I'd agree that the SI equation should be listed before the cgs equation. --ABQCat 02:28, 28 Dec 2004 (UTC)

-- Why, physicists use so many unit system variants and choose what ever system makes the math the easiest for them. My favorite are God's units or natural units

In the sixty-to-eighties a variety of things were settling out. CGS was far more common in many sciences. Prior to everyday available computers (or hand calculators), many problem types were best solved using scale factors appropriate to the range of expected data... one only dealt with the first few significant digits on a slide rule, and/or log tables. Been there, did that! // FrankB 13:54, 12 November 2008 (UTC)

## SI: approximation -> exact???

Here is the approximation from the article:

This can be changed to the following, which is exact, assuming the "cgs equation" is exact.

## Dimensional analysis

Here, we are taking the logarithm of a quantity with units, which is forbidden by the dimensional analysis article. Brianjd 06:24, 2004 Dec 29 (UTC)

So you can't do a full dimensional analysis of all this. Sometimes you just have to accept that this is HOW they do it without understanding WHY they do it this way. I do recall a few times in my engineering classes when we needed to take logarithms of quantities with units - the professors told us not to worry and to just bring the units outside the logarithm. --ABQCat 07:47, 29 Dec 2004 (UTC)
I haven't read it fully because my studies are not advanced enough to understand it, but it doesn't seem to mention any exceptions. So it seems that it needs to be changed. Brianjd 07:42, 2005 Jan 11 (UTC)
After taking the logarithm, you have a quantity with units of the type mass×length²/time², from which you have to subtract a dimensionless number. How do you explain that? One could say that the number has the same units, in which case the final result also has those units, so how is it a "scale"?
Maybe it's a really kludgy way to do this, but maybe the equation WORKS if the value of the moment is in the correct units, but for use in the calculation the units are stripped off? That would eliminate logs of units and subtracting dimensionless numbers. Again, I don't know, but it's possible. --ABQCat 23:29, 11 Jan 2005 (UTC)

The old formulas (prior to 12 June 2005) were an outstanding example of how not to use physical quantities in modern scientific writing. I've decided to be bold and replaced them with an equivalent version that follows the ISO 31-0 convention of using division by a unit when it is necessary to convert a physical quantity into a dimensionfree numerical value. This way, each formula becomes independent of the units used to write down the quantities. No more need to have "SI" indices and similar nonsense. I nevertheless left several forms of the expression standing, using both SI and CGS units in the division, for the benefit of people who are not experienced in converting between CGS and SI. It would be nice is someone finally taught the authors of USGS web sites how to use units properly ... Markus Kuhn 12:45, 12 Jun 2005 (UTC)

Exactly, my first reaction was "what? a logarithm of a dimensioned number?" It's silly too, because there it's unnecessary:

${\displaystyle M_{w}={2 \over 3}log_{10}\left({\frac {M_{0}}{M_{ref}}}\right)}$
with
${\displaystyle M_{ref}=10^{10.7}dynecm=10^{3.7}Nm=5011.87Nm}$

Wouter halswijk (talk) 12:50, 21 January 2010 (UTC)

Unfortunately, geologists (at least those that write these formulae) don't generally care about dimensions, so it isn't technically correct, but will give the correct values, and is the only version available in published sources. OrangeDog (τ • ε) 13:17, 21 January 2010 (UTC)

## Energy example

There was an example which said: sonny For example, M0 = 6,7,8,9 means energies of approximately 1 petajoule (1 PJ = 1015 Joules), 32 petajoules, 1 exajoule (1 EJ = 1018 Joules), 32 exajoules.

I removed it because M0 should increase linearly with energy and Mw was what was probably intended. If I replaced M0 with Mw, the energies didn't match these sources: [1] [2]. Some one else who has more knowledge of this can add it back. Shameer 00:16, 30 Dec 2004 (UTC)

-- At work sometimes I see magnitudes expressed in eqv killo tons of tnt. Maybe we should try it here too, it was a nice representation

Yes, I meant Mw. I changed it, now also taking into account the two conversion factors, as I understand them from the links.--Patrick 11:55, Dec 31, 2004 (UTC)

Seeking support for "The energy is 1/2000 times the moment," I read [3] but remained confused. The "magnitude 6 = 1 megaton TNT" rule in [4] suggests a formula more like

${\displaystyle M_{W}={2 \over 3}\log _{10}E_{\mathrm {SI} }-4.4\,}$

--Mgarraha 22:22, Dec 31, 2004 (UTC)

I hope the rephrased section on kt TNT comparisons makes it clear, that neither earthquakes nor underground nuclear weapons tests release more than a tiny fraction of their total converted energy in the form of seismic waves, and that therefore any comparison between the two is only meaningful if you agree on a seismic efficiency coefficient for the nuclear weapon. That of course depends a lot on the design of the test and the test site. Since all conversion formulas are equally useless and misleading, I find sympathy for the established secret convention of telling any naive journalists who insists on a TNT comparision a conventional figure that is based on magnitude 0 being equivalent to 1 kg TNT. That saves the seismologists unnecessary mental arithmetic on the phone when a journalist really does not want to go away without a TNT figure, and everyone is happy. Markus Kuhn 13:19, 12 Jun 2005 (UTC)

## Formulas

I notice that it was changed from the "preferred" formula to another formula. Why? I quote the following from [5]: "Another source of confusion is the form of the formula for converting from scalar moment M0 to moment magnitude, M. The preferred practice is to use M = (log Mo)/1.5-10.7, where Mo is in dyne-cm (dyne-cm=10-7 N-m), the definition given by Hanks and Kanamori in 1979. An alternate form in Hanks and Kanamori’s paper, M=(log M0-16.1)/1.5, is sometimes used, with resulting confusion. These formulae look as if they should yield the same result, but the latter is equivalent to M = (log Mo)/1.5-10.7333. The resulting round-off error occasionally leads to differences of 0.1 in the estimates of moment magnitude released by different groups. All USGS statements of moment magnitude should use M = (log Mo)/1.5-10.7 for converting from scalar moment Mo to moment magnitude." Anonymous

I suggest we keep for the moment the version with parenthesis where the factor 2/3 is not already multiplied into the offset. This form ensures that the SI and the CGS versions remain consistent without rounding errors when written using a fraction-free decimal offset. Otherwise, the final constant would have to change by the ugly offset of 7*(2/3). In that respect, the above quoted USGS policy is a somewhat unfortunate choice. Let's hope that it is already outdated and that they now finally also use SI, like everyone else. Markus Kuhn 13:00, 12 Jun 2005 (UTC)

So what's the evidence against the USGS formula? Is the alternative form a standard anywhere else? To be clear, I'm not concerned about the units here, I'm concerned about the numeric result. ~brad 9 Feb 2006

## Energy formula inaccurate above 8.0?

I read an article by a local Geology professor stating that the energy released by an 8.5 is over 10 times greater than the energy released by an 8.0.

According to the energy formulas in the article, the energy should only be 5.62 times greater.

I emailed the professor, and she said the simple formula fails for "very large" earthquakes due to:

• a non linear increase in frictional heat release
• free oscillations generated
• impacts on rotation
• permanent deformation

This is all over my head. Is it worth mentioning in the article that the energy formula fails for large earthquakes?

Maybe. I'm not sure that I understand exactly what she meant. I think it depends which energy she is talking about. The total energy release formula is ${\displaystyle {\mathcal {E}}_{r}=-({\mathcal {E}}_{e}+{\mathcal {E}}_{g}+{\mathcal {E}}_{k})}$ where ${\displaystyle {\mathcal {E}}_{e}}$, ${\displaystyle {\mathcal {E}}_{g}}$ , and ${\displaystyle {\mathcal {E}}_{k}}$ represent elastic, gravitational, and kinetic energy. In addition, there is the concept of seismic energy, which is the total released energy minus the energy dissipated by frictional heating of the fault. I am pretty sure that the total released energy is still estimated correctly by the moment. However, the partitioning of the energy may change in the ways the professor noted. When talking about energy here, it's important to know exactly what energy is being referred to. Note: The text I consulted is Theoretical global seismology by Dahlen and Tromp (1998). Gwimpey 18:49, Jan 19, 2005 (UTC)

## Tom Hanks

Tom Hanks is an actor (real name Thomas Jeffrey Hanks) This article points to an article about him, but i think this Tom Hanks is a different person

Thomas C. Hanks is a seismologist at the US Geological Survey in Menlo Park —Preceding unsigned comment added by 71.146.27.92 (talk) 06:40, 14 January 2009 (UTC)

## Wretched formulas (units problem, etc.)

The "Energy" section really sucks: it is both redundant and confusing. For starters, Log(x) only makes sense if x is dimensionless. These formulas should be recast in the form Log(x/x0), where x and x0 have the same dimensions. Give x0 in several different units, and get rid of all but one of the nearly identical equations. Also, give the inverted version of the equation to give energy in terms of moment magnitude -- the more useful direction for the calculation. I'm just passing through, but it would be nice if someone would redo this section from scratch.

I've fixed the unit mess and cleaned up the wretched energy section. I wanted to preserve the underlying information in the latter, so I split it up into separate sections on the energy magnitude and on comparing earthquake magnitudes with TNT-expressed underground nuclear detonations. If people want to keep things short, I'd be happy to agree that both sections could be moved to other articles, with appropriate cross references. If people stopped the silly and utterly meaningless practice of comparing earthquakes with nuclear detonations, that would be even better! Markus Kuhn 13:08, 12 Jun 2005 (UTC)

## Just wondering

what is the difference from a 4.0 on the richter scale to a magnitude of 5.0?

The article explains this very clearly already. Markus Kuhn 23:51, 9 December 2005 (UTC)

Could a table be drawn up to show examples at each part of the scale like the Richter magnitude scale article does? The Basel earthquake says it had a mwm of 6.2, and I have no idea what that means in terms of power. The artcle needs some more for the layman, as right now it's all technical jargon to me.--SeizureDog 14:04, 5 January 2007 (UTC)

I concur. And I don't see anywhere where the comparison with Richter is explained, let alone "very clearly"! How about a small chart giving Richter and Mms values (assuming they are always the same for a given quake, which I can't tell from this convoluted article) and something like destruction or energy released.

## Strange formula

I have noticed that after the main formula the symbols N and m are not explained. Reading previous discussions, I think they stand for Newton and meter to make M0 dimensionless. It doesn't really make sense, since they look like other parameters with their own value, in any case their meaning should be clear from the context and it's not. I would suggest a notation like this:

${\displaystyle M_{\mathrm {w} }={2 \over 3}\left(\log _{10}|M_{0}|-9.1\right)}$
where ${\displaystyle |M_{0}|}$ is the dimensionless module of the seismic moment

About another previous discussion, I absolutely agree that in physics it is not correct to calculate the logarithm of any number that is not dimensionless, but in engineering it is quite common to represent dimension-ful functions with a very wide range using logarithmic scales. For example, the Bode plot of a voltage-to-current amplifier is the plot of a dimension-ful number [A/V] on a logarithmic scale. There is no problem in taking the logarithm of a dimension-ful number, as long as it's only for measuring or plotting sake. I can agree that the best scales use a reference to make the argument of the logarithm dimensionless (e.g. dB spl: Tom Hanks and Hiroo Kanamori didn't make their scale properly from this point of view. We could fix it writing like:

${\displaystyle M_{\mathrm {w} }={2 \over 3}\left(\log _{10}{\frac {M_{0}}{M_{r}}}-9.1\right)}$
where ${\displaystyle |M_{0}|}$ is the dimensionless module of the seismic moment and ${\displaystyle M_{r}}$ is the reference value of 1 Nm

but it would be original work, I guess (even if it's definitely more rigorous then the original) Alessio Damato (Talk) 10:40, 17 August 2007 (UTC)

I think the formula is currently expressed very well and should not be changed as you suggest. It currently follows the stylistic guidelines given in various International Standards related to scientific notation (e.g., ISO 31-0, SI Brochure, etc.), which specify that variable quantities are distinguished typographically from units and other constants by use of italic characters. ISO 31-0 also specifies that a quantity is always a product of a number and a unit, and if you need a dimensionless number, you can simply access that by dividing the quantity through the unit in which you want the number to express the quantity. The current formula also uses the well-understood international standard symbols for the units used in the correct font. All these are world-wide very well-established conventions in scientific writing, that are globally taught in most secondary-school physics classes. I personally find them pretty convenient, logical, and easy to understand. On the other hand, I find your first alternative formula confusing, as it suggests calculating the logarithm of an energy quantity, which physically makes no sense. Your second formula is identical to the current one after the substitution Mr = 1 Nm, and therefore the current formula should be just as good as your second alternative. It simply avoids the unnecessary introduction of another, redundant quantity Mr. I suspect it all boils down to that you might not have been familiar with the (pretty common) typographic convention that units of measurements are not typeset in italics (NIST SP 811, etc.). Markus Kuhn 12:23, 18 August 2007 (UTC)
well, as you like, but I'll point out clearly in the description that they are not parameters with their own value. Alessio Damato (Talk) 15:06, 18 August 2007 (UTC)
Markus, I don't think the confusion was with the font. The confusion was with the notion of dividing by a unit. The concept that "if you need a dimensionless number, you can simply access that by dividing the quantity through the unit in which you want the number to express the quantity" is, I believe, not widely appreciated by educated adults in the U.S. It does make sense when you think about it, however. I have added a sentence explaining the notation. Mark Foskey (talk) 02:48, 14 May 2008 (UTC)
I see. I would have expected the notion to be pretty familiar and clear to most people in Europe who have enjoyed some form of secondary-school education in physics. But I admit that I do notice occasionally that some American authors do things with units that I would consider rather odd and cumbersome, possibly because they have not grown up with thinking of them just as factors that can be divided or multiplied like any other factor, or because an algebraic way of using units is not commonly taught there. I was taught that writing formulas like
F = m · a, where F is in newtons, m is in kilos and a is in m/s2
is bad style, as the units should always sort themselves out algebraically on their own in physical formulas. One should therefore never have to explicitly say which variable is measured in which unit, as they are just quantities that work no matter what the unit is. Only in ad-hoc scales that require logarithms, it actually becomes necessary to explicitly divide through a particular unit, as the formulas in this article do. Is the algebraic use of physical units only widely taught in countries that use mostly SI units and can we therefore not just simply assume familiarity with it in Wikipedia articles about scientific topics? Markus Kuhn (talk) 14:08, 14 May 2008 (UTC)
While checking the sources I noticed that the equation was in fact completely wrong regarding the brackets, and ${\displaystyle M_{0}}$ should be given in dyne centimetres.[6] I have change it to reflect the original paper, and explained the terms. –OrangeDog (talkedits) 02:53, 29 January 2009 (UTC)

## Richter Scale Inconsistency?

The article about the Richter Scale has the following:

The energy release of an earthquake scales with the 3⁄2 power of the shaking amplitude, and thus a difference in magnitude of 1.0 is equivalent to a factor of 31.6 in the energy released; a difference of magnitude of 2.0 is equivalent to a factor of 1000 in the energy released.

...the Richter Scale, which has a 10¹ = 10 times energy increase for a 1 step increase, and 10² = 100 times energy increase for a 2 step increase. Instead, an increase of 2 steps corresponds to a 10³ = 1000 times increase in energy.

If I assume the information about the Richter Scale in the Richter Scale article is accurate, it appears an editor of this article has confused amplitude with energy when referring to the Richter Scale. SlowJog (talk) 16:23, 13 May 2008 (UTC)

I found a USGS page that discusses the Richter magnitude scale and specifically states, "each whole number step in the magnitude scale corresponds to the release of about 31 times more energy than the amount associated with the preceding whole number value." This page was part of the external links on the Richter magnitude scale page, I changed it to a citation.

Another USGS page states, "All of the currently used methods for measuring earthquake magnitude (ML, duration magnitude mD, surface-wave magnitude MS, teleseismic body-wave magnitude mb, moment magnitude M, etc.) yield results that are consistent with ML. In fact, most modern methods for measuring magnitude were designed to be consistent with the Richter scale." Added this as an external link on the Richter magnitude scale page. Gblandst (talk) 17:43, 13 May 2008 (UTC)

## On {{confusing}}

• <*--

• DITTO, what he/she says!!! ... this is unfamiliar subject... comparisons needed! WORSE, the above comments have been asking for such for several years. Come on folks... is that professionalism at it's best!?? // FrankB 14:15, 12 November 2008 (UTC)

## "Compared to Richter Scale"

I am just a layman who came to this page because an earthquake on the Main Page was described on the "moment" scale, and I wanted to know how "moment" scale values would corrolate into (to me) more familiar Richter scale. I was eventually able to find this information, although sort of buried beneath some very confusing mathematics. So, I added a section heading in hopes that information will be easier for future lay inquirers to find. Maybe the math equations should be moved lower in the article, rather than being the first thing your eye sees? I'm sure that, like me, they don't really convey any information at all to most people. —Preceding unsigned comment added by Blorblowthno (talkcontribs) 21:02, 15 October 2008 (UTC)

I took the silence on this issue for tacit consent, and have now gone ahead and moved the mathematical derivation lower down in the article. Blorblowthno (talk) 19:44, 29 October 2008 (UTC)
The section fails to specify whether quoted values are on MMS or Richter or both. Some examples values in the ranges where the scales differ would also be useful. OrangeDog (talkedits) 00:04, 10 January 2009 (UTC)
Making up sample values is getting more into original research. It seems like that would be counter intuitive as well, because it would imply that the two scales have different magnitude values for the part of the scale where they overlap. This is wrong as far as I can tell; Local Magnitude and Moment Magnitude agree within the 3.0-7.0 or 3.5-7.0 range, and beyond that range you would only use one or the other (RMS for < 3, MMS for > 7). Thus when the article says 6.0, you can take that to mean the same thing on both scales (as it says). BigNate37(T) 22:42, 10 January 2009 (UTC)
This explanation should be included in the article somewhere. I still think a small table or possibly a graph could show this explicitly with a few sample values across the ranges you mentioned.–OrangeDog (talkedits) 22:34, 11 January 2009 (UTC)
That graphic indeed makes no sense. What is it supposed to be showing? The differing gradients are both imprecise and unexplained. A line graph or x-y scatter would probably be better for whatever it's supposed to be. –OrangeDog (talkedits) 02:01, 26 January 2009 (UTC)
OrangeDog, thanks for continuing the conversation here. I'll tell you what I was trying to get at with the graphic, and maybe we can figure out a better way of representing it visually. Basically, the big issue on this article has always been, people want to know how to "convert" from Richter values to Moment Magnitude values. But that way of thinking is a fallacy. The scales are designed to dovetail together along the same continuum. The Richter "scale" and the Moment Magnitude "scale" aren't really different scales at all, but different mathematical formulae for computing values along that continuum. So, we can talk about a magnitude 9 earthquake... you'd never use the Richter formula to compute a magnitude estimate for that earthquake, because it's too big. With the Richter formula, no matter how large of inputs you use, your output will max out around 7.5. So, for a very large earthquake, you want to use the Moment Magnitude scale. Now, there's no sharp point where the Richter scale "stops" working and you "start" using Moment Magnitude. Just, as the earthquakes get larger and larger, the Richter formula becomes less and less helpful. In the same way, as earthquakes get smaller and smaller, the Moment Magnitude formula becomes less and less helpful. So, what I'm trying to show with the graphic is the ranges where the different "scales" are best suited/most helpful/most appropriate. —Preceding unsigned comment added by Blorblowthno (talkcontribs) 23:45, 27 January 2009 (UTC)
In response to BigNate37, deriving mathematical truth from published equations in not WP:OR. No-one would have any problem including that ${\displaystyle \sin(2.124)=0.851}$ if it were relevant, but it would be nearly impossible to find a verifiable source that explicitly states it. –OrangeDog (talkedits) 02:15, 26 January 2009 (UTC)

Re-wrote the section to simplify and include examples. Hopefully much clearer now. –OrangeDog (talkedits) 02:49, 29 January 2009 (UTC)

Please list values for both scales in the table here:
Richter_magnitude_scale#Examples
The recent quake in Japan is listed as 9.0 on the Richter scale. Is it listed accurately? Would the value be higher or lower on the moment magnitude scale?- 71.179.126.205 (talk) 23:04, 10 April 2011 (UTC)
Where is the Japan earthquake listed on the Richter scale? The Richter scale has not been in use for at least 30 years. OrangeDog (τ • ε) 18:08, 11 April 2011 (UTC)
Under the "Richter Approximate Magnitude" heading on the "9.0" line: Sendai earthquake and tsunami (Japan), 2011. The M_W prefix may mean moment magnitude scale, but then the heading in the table of the article with the same name is misleading. - Ac44ck (talk) 02:03, 12 April 2011 (UTC)
It's linked to moment magnitude scale. The Richter scale is not the problem, it's the observation using the 20 second period on the seismometer that is the problem - the scale itself has no upper limit, and Mw was designed to match Richter for lower magnitudes, so what the table is saying is that the recent earthquake has the equivalent power of a 9.0 on the Richter scale, even if it couldn't be measured in that way. Mikenorton (talk) 11:01, 12 April 2011 (UTC)
If it was 9.0 on the Richter scale, then what was it on the moment magnitude scale? Is it true that the "big ones" have higher numbers on the moment magnitude scale than they would on the Richter scale? - Ac44ck (talk) 03:37, 13 April 2011 (UTC)
It wasn't a 9.0 on the Richer scale. The article has since been corrected to remove all mention of Richter scale, which is never used except by lazy journalists. OrangeDog (τ • ε) 17:44, 13 April 2011 (UTC)
This seems confusing to me:
• A column labeled "Richter Approximate Magnitude" in the Richter magnitude scale contains no values in the Richter magnitude scale?
• Some entries have no prefix: Lincolnshire earthquake (UK), 2008
• Some entries have the M_w prefix: Ontario-Quebec earthquake (Canada), 2010
• Some entries have an M_s prefix: Caracas earthquake (Venezuela)
Is an apples-to-apples comparison not doable?
Is it true that the "big ones" have higher numbers on the moment magnitude scale than they would on the Richter scale? - Ac44ck (talk) 04:19, 14 April 2011 (UTC)

## Clarifying What the Values mean.

This article is still completely useless at explaining what a value on the scale actually means. Therefor I'm going to post a table from the Richter Scale article and maybe we can adapt it to the moment magnitude scale. If this works it can be inserted into the article. Comments? --Arnos78 (talk) 22:48, 1 June 2009 (UTC)

Yes the scales give similar values so this would work well in this article, although generally moment magnitude is not used for quakes less than M3.5. RapidR (talk) 23:06, 1 June 2009 (UTC)

Richter Magnitudes Description Earthquake Effects Frequency of Occurrence
Less than 2.0 Micro Microearthquakes, not felt. About 8,000 per day
2.0-2.9 Minor Generally not felt, but recorded. About 1,000 per day
3.0-3.9 Often felt, but rarely causes damage. 49,000 per year (est.)
4.0-4.9 Light Noticeable shaking of indoor items, rattling noises. Significant damage unlikely. 6,200 per year (est.)
5.0-5.9 Moderate Can cause major damage to poorly constructed buildings over small regions. At most slight damage to well-designed buildings. 800 per year
6.0-6.9 Strong Can be destructive in areas up to about 160 kilometres (100 mi) across in populated areas. 120 per year
7.0-7.9 Major Can cause serious damage over larger areas. 18 per year
8.0-8.9 Great Can cause serious damage in areas several hundred miles across. 1 per year
9.0-9.9 Devastating in areas several thousand miles across.
1 per 20 years
10.0+ Epic Never recorded; see below for equivalent seismic energy yield.
Extremely rare (Unknown)

(Based on U.S. Geological Survey documents.)[1]

Changing this to use MMS would be complete synthesis. You would need a source that explicitly describes the effects of earthquakes of differing magnitude. Even in itself this table isn't very useful, the distinctions being drawn are done so pretty arbitrarily (compare a 4.9 to a 5.0 for example). The moment magnitude scale isn't based on destructive effects or actual shaking of the ground. OrangeDog (talkedits) 08:54, 2 June 2009 (UTC)

No, this is perfectly appropriate for MMS. In fact, as the table refers to magnitudes greater than 7 which are impossible to measure on the classical bodywave Richter scale, it is either probably based on MMS (or a surface wave magnitude scale). Remember, MMS values are 1) designed to roughly mimic the values originally used in the Richter scale, 2) provide the capability to measure earthquakes larger than 7, which classical body-wave amplitude based magnitude measurements cannot do, and 3) relate the magnitude of an earthquake to the size of the rupture. There is no reason to "compare" Richter and MMS*. They are the same thing, as best as Hanks and Kanamori could do within the constraints and within the error of the estimates, which are substantial. Given that true "Richter" magnitudes have not been calculated since the Wood-Anderson seismometer became obsolete (1960's), anyone who thinks they are familiar with the "Richter scale" is mistaken, unless they are referring to the general idea of classifying earthquake size by a small number typically in the range of 2 to 9. This needs to be clarified in the article, and I may try. *Unless you are estimating magnitude/frequency relationships from old catalogs in southern California or some other esoteric pursuit. 146.244.227.220 (talk) 23:49, 6 January 2010 (UTC)

Note the problems in your use of "probably" and "roughly". OrangeDog (τ • ε) 13:12, 21 January 2010 (UTC)

## citations

I removed the "unreferenced section|date=March 2010" from the section on comparing magnitudes, because the work is shown and requires only high school algebra to verify. Learjeff (talk) 17:13, 14 March 2011 (UTC)

It also requires references to establish that the content is relevant and not WP:UNDUE. As well as claims as to the closeness of the relationship. OrangeDog (τ • ε) 22:39, 14 March 2011 (UTC)
Odd, OrangeDog, that you should demand references proving the relevance of comparative magnitudes. Never mind that comparing magnitudes is a perfectly reasonable thing for people to wish to do, and therefore a perfectly reasonable thing for them to hope to learn about in Wikipedia. What's odd is that the article did have just such a reference(<ref name="AP-CHILE-HAITI">{{cite web | last = Bajak | first = Frank | title = Why Chile dodged Haiti-style ruin | publisher = [[Toronto Star]] | date = 28 February 2010 | url = http://www.thestar.com/news/world/article/772765--why-chile-dodged-haiti-style-ruin | accessdate = 2010-02-28}}</ref>) until, at 23:41 on 21 Mar 2010, it was deleted by you.
That anyone would have demanded references "to establish the purpose of the equation" I don't understand. Its purpose is made crystal clear by the title and the body of the section that contains it.
Indeed, to what would you have a footnote proving relevance affixed? Certainly not to the equation itself, which is relevant (on its face) to the sentence containing it. Would you have a new purpose-built sentence added, "One way people try to make sense of magnitudes is by comparing them from one earthquake to another [but you needn't take our word for it because we offer you a reference to prove it]"?
As you can see from the summary, I removed the ref as part of an "unnecessary recentist example". While it is a good reference, there is nothing in this article that it can directly verify. What I'm looking for is a reliable secondary source that verifies the equation in question to be "closely related" and "allows one to assess the proportional difference fΔE in energy release between earthquakes of two different moment magnitudes". The title and body of the section do make it clear, but they are not verifiable. I would suggest that such a reference goes when I had placed the {{cn}}. OrangeDog (τ • ε) 20:55, 17 March 2011 (UTC)
The "unnecessary recentist" I understood and accepted (I don't agree with it, but I can live with it). The close relationship of which you aren't yet convinced—or anyway desire third-party confirmation—is straightforward high-school algebra, as Learjeff wrote above and the text makes plain: you start with the definition (the equation starting with MW = ...) and solve it for M0. That's what's in the numerator and in the denominator, which represent the two quakes being compared. And since the numerator and denominator are both in terms of energy, the ratio connotes proportional energy. QED.
As to making it clear that this is kosher, the Toronto Star reference first shows up in an even earlier version of the article that worked through one of those recentist examples, both to help any math-challenged readers and to provide verification. That version says, "As seismologists reported,[5], the Chilean quake released roughly 500 times as much energy as the Haitian quake. That comparison works out as follows: fΔE = 10(3/2)×1.8 ≈ 501." That was a better place to put the reference, but the example got removed by editors who thought it was too much hand holding.—PaulTanenbaum (talk) 00:38, 18 March 2011 (UTC)
One can create any equation they wish using simple algebra. I could likewise construct an equation relating the magnitude of an earthquake with the weight of peanuts that would release the same amount of energy should they undergo nuclear fission. Without an actual specific and reliable source, this article disintegrates into a long list of pointless (and often wrong) equations. OrangeDog (τ • ε) 00:03, 22 March 2011 (UTC)
You enumerate above two expectations of the desired reliable secondary source: (1) that it verify "the equation in question to be 'closely related,'" and (2) that it verify that the equation allows one to assess the proportional difference in energy release between earthquakes. As to (1), would you demand a reference to justify an article's describing the equation m = F/a as closely related to the equation F = m a? And as to (2), the section in question explains that the algebra solves the earlier equation for M0, which (as the definition explains) has units dyn · cm (i.e., energy), so taking the ratio of two different M0 values gives you a proportional comparison of energies; for what part of that logic do you require verification? I am just not seeing the problem, and your peanut-fission example, though perhaps cute, does not help clarify your concern.—PaulTanenbaum (talk) 21:13, 29 March 2011 (UTC)
Actually, yes I would, unless it was an article on elementary algebra. There is no evidence that the equation in question in this article is relevant, important or correct, in decreasing order of concern. OrangeDog (τ • ε) 21:16, 31 March 2011 (UTC)

## Converting magnitude to energy

The formula in this section does no appear to be correct. For a magnitude 4 earthquake I get 56 GJ, not 1 PJ. I used the expressions ${\displaystyle M_{\mathrm {w} }=\textstyle {\frac {2}{3}}\log _{10}M_{0}-10.7,}$ and ${\displaystyle {E}=M_{0}/(2\times 10^{4})\,\!}$, both from here for the energy in dyne cm, dividing by another 107 to convert to joules. My values match others that I've found in this linked powerpoint file. Mikenorton (talk) 22:30, 18 March 2011 (UTC)

So do I. As it's unreferenced, and with an insufficient definition of energy, I'm removing it. OrangeDog (τ • ε) 00:14, 22 March 2011 (UTC)

## The problem of "energy" related to earthquakes and magnitudes

I see from the text and the discussions that there exists a confusion about what is "energy". As the articles states correctly, elastic energy is released during a rupture of a fault. This energy goes into fracturing rock, generating heat, and energy radiated as seismic waves Es. Es can be measured by integrating the spectrum of the radiated waves. Because this requires extra work, Es is often estimated from one of the magnitudes, using an empirical equation. However, that is not quite correct. Most of the energy resides in high frequency waves, and especially in the "corner frequency". There are eqs with relatively large mb and low Mw. These are high stress drop events. Generally Es is best estimated from mb, and NOT from Mw, because the latter is based on very long period, low energy waves. Perhaps I should take the trouble to explain this somewhere.

I have introduced changes in several places in the text of the eq project, trying to get away from saying magnitude measures energy (because that is not quite correct) and saying "magnitude measures the size of an eq". That is avoiding the issue whether or not Es is considered or the entire elastic E released by an earthquake. The moment, Mo, has units of energy because it measures the work done.

Of course there are many technical articles to cite, we do not need to go to a ppt-file lecture notes.

QUESTION: Should I explain this, or is someone going to remove what I write? If the latter is the case, I do not want to spend the time.MaxWyss (talk) 07:22, 18 April 2011 (UTC)MaxWyss

What you've written so far is really good. As long as you continue to cite any possible points of contention, go right ahead. I think the Richter comparison section could do with some of its content being moved to a "History" section as much of it isn't really about Richter any more. OrangeDog (τ • ε) 19:02, 18 April 2011 (UTC)

## Thoughts on edit as of October 2012

After listening to an introductory geology lecture in which a Ph.D. geologist was unable to put the moment magnitude scale into perspective, I took a shot at some words to make this more easily understood (and pulled the discussion earlier into the article). Am running out of time today, but will come back to pull the excellent material from the comparison with the Richter scale a bit forward into the article as well. Think this is another face of the continuing Wikipedia struggle between providing something for the unexpert reader and providign solid technical material for the more expert user. As always, if I get it wrong, Wiki my work... Skaal - Williamborg (Bill) 23:25, 30 October 2012 (UTC)

## Mw is not moment magnitude

Unfortunately, it has become common for seismologists to refer to "Moment Magnitude" as Mw. This is incorrect and Wikipedia should correct this. The following is the correct vocabulary Hanks and Kanamori (1979) introduced the Moment Magnitude scale and they called it M. Actually it's a capital script M. They defined M == 2/3 (log M0 - 16.05) where M0 is moment in dyne-cm. This is THE definition of Moment Magnitude. Here's where it came from. Thatcher and Hanks (1973) pointed out that there was a general relationship between moment and local magnitude, Ml, that could be written Ml =~ 2/3 (log M0 - 16). In 1978, Kanamori published his paper on energy magnitude Mw, where he argued that it makes most sense to measure the size of an earthquake using its radiated energy. He used the W as meaning energy; he did this even though W often is used for strain energy density in mechanics. Radiated energy and strain energy are definitely different quantities. At any rate, Kanamori's definition of Mw is Mw == 2/3(log W0 - 11.8) where W0 is total radiated energy in ergs (M0 is a torque and W0 is an energy). In that same paper, Kanamori recognized that it's very difficult to estimate W0, so he said that you could estimate W0 using the following approximate relationship between W0 and M0; W0 =~ M0 * 5 * 10**-5. If you replace W0 with the approximate M0 in Kanamori's relation, then Mw =~ 2/3 (log M0 - 16.1). Note that this is an approximation for Mw. After Kanamori published his 1978 paper, Hanks noted that the 1973 Ml relationship with M0 was the same as the 1978 Kanamori relationship between Mw and M0, except that Thatcher and Hanks had a constant of 16 and Kanamori used 16.1. Hanks convinced Kanamori to write a paper to define a scale based on moment. The constant used in the Hanks and Kanamori is 16.05, which was a political compromise. The rest should history, except that somehow it has become common to call Mw moment magnitude. To further complicate the issue, seismic moment is not really a unique measure of an earthquake's size. This is a long and technical issue, but the bottom line is that average slip times the rupture area is indeed a physical parameter (called potency), whereas multiplying potency times the local rigidity (the definition of seismic moment) results in a parameter that cannot be uniquely determined. Please fix this site. It is perpetuating a common misunderstanding. Heatoncaltech (talk) 22:58, 24 January 2013 (UTC)

As you say it has become common to use Mw (much more common than M in my experience) and Wikipedia has to follow usage rather than to try and change it I'm afraid. Mikenorton (talk) 23:09, 24 January 2013 (UTC)

## Vandalism

The section "The Richter scale; a former measure of earthquake magnitude" appears to have been vandalised after the final sentence. I attempted to remove this, but don't seem to be able to as the text does not appear when I try to edit.

Here's a screen shot I did of the section. The only Photoshop work I performed was to highlight the text. [7]

Bwob (talk) 22:03, 10 September 2013 (UTC)

I'm going to guess that it was a cache problem, leaving you viewing an old version of the page, before the vandalism was reverted by ClueBot just a minute after it was added. I looked at it and had the same problem, but I noticed a typo and when I saved that edit, the page updated. Mikenorton (talk) 22:37, 10 September 2013 (UTC)