Talk:Seismic moment

Relations between seismic moment and "energy released by an earthquake"

How is the seismic moment related to the energy released by an earthquake? AxelBoldt 00:58, 26 Dec 2004 (UTC)

I think it pretty much IS the energy release. Note that the units, Newton metres, are equivalent to Joules. 128.232.228.174 (talk) 14:29, 20 May 2008 (UTC)

The physical relation between seismic moment and energy released is indirect, approximate and depends on parameters that have large uncertainties. Describing seismic moment as a measure of the energy released by an earthquake perpetuates misconceptions.

Despite its units being Joules (N.m), seismic moment is not really a measure of energy released. From the body force representation of seismic sources and from the definition of the term "moment" in mechanics, seismic moment is associated to a torque (which also has units of N.m), more naturally than to an energy. Despite J and N.m being the same units, to avoid confusion the usage in mechanics is N.m for torques and J for energies.

Moreover, the term "energy released" is ambiguous. It can refer to the potential energy drop caused by an earthquake ($\Delta W$) but is also, often implicitly, associated to the radiated energy ($E_{R}$). On the one hand, the potential energy drop is approximately

$$\Delta W\approx {\overline {\sigma }}AD$$

where ${\overline {\sigma }}$ is the average absolute stress on the fault (e.g. equation A3 of Venkataraman and Kanamori JGR 2002). Considering the definition of seismic moment, we get

$$\Delta W\approx {\frac {\overline {\sigma }}{\mu }}M_{0}$$

Currently, there is no technology to measure absolute stresses at all depths of interest or method to estimate it accurately, thus ${\overline {\sigma }}$ is poorly known. It could be highly variable from one earthquake to another. Two earthquakes with identical $M_{0}$ but different ${\overline {\sigma }}$ would have released different $\Delta W$. On the other hand, radiated energy is approximately related to seismic moment by

$$E_{R}\approx \eta _{R}{\frac {\Delta \sigma _{s}}{2\mu }}M_{0}$$

where $\eta _{R}$ is radiated efficiency and $\Delta \sigma _{s}$ is the static stress drop (e.g. from equation 1 of Venkataraman and Kanamori JGR 2002). These two quantities are far from being constants. For instance, $\eta _{R}$ depends on rupture speed; it is close to 1 for regular earthquakes but much smaller for slow earthquakes (e.g. a tsunami earthquake). Two earthquakes with identical $M_{0}$ but different $\Delta \sigma _{s}/2\mu$ would have radiated different $E_{R}$. In summary, the seemingly simple linear relations between seismic moment, potential energy drop and radiated energy have uncertain (and most likely variable) pre-factors. Hence, there is no solid basis for associating $M_{0}$ with "the energy released by an earthquake" without adequate caution. Ampuero (talk) 02:37, 6 August 2017 (UTC)

Clarification needed

@Ampuero: Hi Pablo. So almost two years on, and I think I'm starting to understand some of this. But there are still some points on which I could use some clarification, if you should have a little time to spare. (These arise from what I am working on at moment magnitude scale, but it seems more appropriate to discuss them here.)

Keiiti Aki is widely credited for "introducing" the standard equation by which seismic moment is generally defined. Often there is an implication that he invented (discovered?) the concept of seismic moment. However, Deichmann (2006) says "seismic moment was first derived theoretically from dislocation theory by Vvedenskaya (1956) ...." That seems likely, if "seismic moment" is taken as the magnitude of the double-couple. So does the concept of seismic magnitude pre-date Aki's 1966 papers? Did he only derive the equation for relating it to the physical parameters, or was the concept and term new with him? ♦ J. Johnson (JJ) (talk) 20:49, 29 March 2019 (UTC)

Do you have a PDF of Vvedenskaya (1956)? Ampuero (talk) 21:48, 29 March 2019 (UTC)

No. Is that article by any chance in English? ♦ J. Johnson (JJ) (talk) 23:34, 29 March 2019 (UTC)

I've never heard about that paper before. Most likely the original is in Russian and I don't know if it has been translated or was availabe to Aki. I don't know if Vvedenskaya's paper, like several papers cited by Aki 1966, developed the theory of dislocations for earthquakes but without introducing the seismic moment as we know it. Aki 1966 paper shows awareness of other people's work: see his note #10 referring to a previous erroneous attempt by other authors. Ampuero (talk) 07:15, 30 March 2019 (UTC)

Yes, at the bottom of page 84. (I have been studying that and the previous page fairly closely.) I think Aki agreed with Maruyama (1963), Haskell (1964), and Burridge & Knopoff (1964) (see Aki's notes 7, 8, and 9). I've looked at those papers, and while the math is mostly beyond me I haven't recognized anything that looked like "seismic moment", or (this should be checked) moment magnitude.

I think you would be interested in a very nice review by Udías 1991, "Source Mechanism of Earthquakes". Extensive, but not too deep (why, there are large parts that I think I understand!). He describes some of Vvedenskaya's work, and cites several papers (some in Russian), but I haven't seen any of them. Nor anything by Nabarro or Steketee. ♦ J. Johnson (JJ) (talk) 21:59, 30 March 2019 (UTC)