I used Wells & Coppersmith, (1994) paper (has 4417 citations) to determine the rupture width and length when the moment magnitude (Mw) was given. This paper is little bit old paper. I did not find any new paper of ground breaking idea against this paper. Do you use another approach to calculate the rupture width formulas published by Wells & Coppersmith, (1994)? I know that the theoretical way is too complex. I am searching a simple procedure (empirical or semi empirical).
Dear Sameera,
I have listed out two references where you can find the relationship between seismic parameters.
1) "Relationships between moment magnitude and fault parameters: theoretical and semi-empirical relationships" by W. Haiyun and T. Xiaxin, 2003
2) "Estimating Surface Rupture Length and Magnitude of Paleoearthquakes
From Point Measurements of Rupture Displacement" by GP Biasi and RJ Weldon II, 2006.
Hope this will be helpful for you.
These relationship are more recent:
Leonard (2010). Earthquake Fault Scaling: Self-Consistent Relating of Rupture Length, Width, Average Displacement, and Moment Release. Bulletin of the Seismological Society of America, Vol. 100, No. 5A, pp. 1971–1988, doi: 10.1785/0120090189
Leonard (2012). Erratum to Earthquake Fault Scaling: Self-Consistent Relating of Rupture Length, Width, Average Displacement, and Moment Release. Bulletin of the Seismological Society of America, Vol. 102, No. 6, pp. 2797–2797, doi: 10.1785/0120120249
We use also a combination of Wells&Coppersmith (1994), and Geller (1976) with a limitation on the width for giant earthquakes for which the aspect ratio becomes longer and longer (the width is limited to the interface between the ocenic plate and the continent in the subduction zones). The fault dimensions such estimated from the scalar seismic moment work surprisingly well in the numerical tsunami simulations that we have computed. I shall see at the new scaling laws (thank you for the new references), but we may consider that the old good papers stay still good papers.
See theses papers (available on my page):
Rapid forecast of tsunami wave heights from a database of pre-computed simulations, and application during the 2011 Tohoku tsunami in French Polynesia, Reymond & al., GRL, 2012.
and
New Tsunami Forecast Tools for the French Polynesia Tsunami Warning System Part II: Numerical Modelling and Tsunami Height Estimation, Jamelot & Reymond, PAGEOPH, 2015.
You can not get rupture length and area from magnitude [or moment] but you can estimate magnitude from rupture length and/or rupture area.
Dear Sameera,
The research on scaling relationships between earthquake rupture parameters has advanced significantly in the more than twenty years elapsed since the paper of Wells & Coppersmith (1994).
These improvements are based on datasets which are larger than the one in W&C, and which also embrace a wider range of faulting types and tectonic environments.
For example, the W&C dataset was biased, since it was dominated by earthquake ruptures with low stress drop. In consequence, for a given rupture length, earthquakes with large stress drops have magnitudes larger than expected from the W&C relations (for example the 2011 Darfield earthquake in New Zealand).
The best reference I can recommend is this review:
Stirling, M.; Goded, T.; Berryman, K. & Litchfield, N. (2013) Selection of earthquake scaling relationships for seismic‐hazard analysis. Bulletin of the Seismological Society of America, 103, 2993-3011.
Regarding the works by Leonard (2010 & 2012), mentioned in a different answer, note that these self-consistent relationships were recently updated by the same author:
Leonard (2015) Self-consistent earthquake fault-scaling relations: Update and extension to stable continental strike-slip faults. Bulletin of the Seismological Society of America, 104, 2953-2965.
I hope this helps. Best regards,
Álvaro
These and similar papers are usually used to estimate magnitude from fault rupture parameters. Starting from magnitude to "calculate" fault rupture length and width seems problematic, sounds like a very difficult inverse problem.
Lalliana, I agree that it might be problematic but calculating rupture length from magnitude is common in many engineering and research applications. For instance, in rapid loss estimation you initially have only the magnitude and you have to estimate ground motion distributions. Then you need such empirical relationships because most GMPEs use distance from the surface projection of the fault rupture. Similarly if you are doing Coulomb stress analysis on large catalogs, where you can't study each earthquake individually, you need a proxy for the source lengths.
I agree! The question is more complete with the "purpose". I think the purpose is very important as it has a direct bearing on how it should be handled.
For real pro-earthquake rapid-loss estimation --- magnitude being given [by a network operator] and identified the source/fault --- the published correlations should be helpful.
Please consider my earlier comment only for pre-earthquake purposes.
Anyone could suggest a reference about the above-mentioned relationship between fault rupture dimensions and earthquake magnitude which is applicable specifically to the Himalayan region?
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