Scaling relations for energy magnitudes
Article Sidebar
Main Article Content
Abstract
Homogenizing earthquake catalogs is an effort critical to fundamentally improving seismic studies for next-generation seismology. The preparation of a homogenous earthquake catalog for a seismic region requires scaling relations to convert different magnitude types, like the mb and Ms, to a homogenous magnitude, such as the seismic moment scale, Mwg, and energy magnitude scale, Me. Several recent studies addressed the preparation of homogenized earthquake catalogs, usually involving the estimation of proxies of moment magnitude Mw from local, ML, and teleseismic (Ms and mb) magnitude estimates. Instead of the standard least squares (SLR), most of such studies used the general orthogonal regression (GOR), while some used the Chi-square regression method. Here we critically discuss GOR and Chi-square regression theory and find that both are the same for the linear case — as expected since both stem from the same mathematical concept. Thus to foster an improved understanding of seismicity and seismic hazard, we used GOR methodology and derived global scaling relations individually between body, surface, energy, and seismic moment magnitude scales. For that purpose, we have compiled 13,576 and 13,282 events for Ms from ISC and NEIC, respectively, mb magnitude data for 1,266 events from ISC, 614 events from NEIC, and Mwg magnitude values for 6,690 events from NEIC and GCMT. We have also derived MS,ISC-to-Me and MS,NEIC-to-Me conversion relations in magnitude ranges of 4.7≤MS,ISC≤8.0 and 4.5≤MS,NEIC≤8.0, respectively. Likewise, we obtained mb,ISC-to-Me and mb,NEIC-to-Me conversion relations for ranges of 5.2≤mb,ISC≤6.2 and 5.3≤mb,NEIC≤6.5. Since the number of data points was insufficient to derive the relations, we considered mb,NEIC up to M6.5. Finally, we derived an MWg-to-Me conversion relation for the 5.2≤Mw≤8.2 range of magnitudes with focal depths <70 km. Our scaling relations can be used for homogenizing earthquake catalogs and conducting seismicity and seismic hazard assessment studies with enhanced realism.
ARK: https://n2t.net/ark:/88439/x063005
Permalink: https://geophysicsjournal.com/article/304
Article Details
Authors who publish with this journal as of Vol. 63 agree to the following terms:
a. Authors share the copyright with this journal in equal parts (50% to the journal, 50% to the lead author), and grant the journal right of first publication, with the work after publication simultaneously licensed under Creative Commons Attribution License CC BY-NC-ND 4.0 that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
b. Authors may enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal, and a reference to this copyright notice.
c. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) during the submission process, as this can lead to productive exchanges and earlier and greater citation of published work and better sales of the copyright.
Author Self-archiving
Authors retain copyright and grant the Journal of Geophysics right of first publication, with the work three years after publication simultaneously licensed under the Creative Commons BY-NC-ND 4.0 License that allows others to share the work (with an acknowledgment of the work's authorship and initial publication in this journal), except for commercial purposes and for creating derivatives.
Authors can enter into separate, additional, but non-commercial contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository, but not publish it in a book), with an acknowledgment of its initial publication in this journal.
Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) before and during the submission process, as that can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
Additional Notes
This journal is one of a handful of scholarly journals that publish original scientific works under CC BY-NC-ND 4.0 - the only Creative Commons license affording the authors' intellectual property absolute worldwide protection.
Journal of Geophysics is published under the scholar-publishers model, meaning authors do not surrender their copyright to us. Instead, and unlike corporate publishers like Elsevier or Springer Nature that resell copyright to third-parties for up to $80,000 (per paper, per transaction!), the Journal of Geophysics authors share copyright equally with this journal.
Therefore, all the proceeds from reselling copyright to third parties get shared to equal parts (50% to the journal, 50% to the lead author). Under the Berne Convention, this protection is an inheritable right that lasts for as long as the rightsholder lives + 50 years.
By submitting to this journal, the lead author, on behalf of all co-authors, grants permission to this journal to represent all co-authors in negotiating copyright sales and collecting proceeds. The lead author should negotiate with his/her co-authors the modalities of distributing the lead author's portion of the proceeds. Usually, this is per pre-agreed percentage of each co-author's contribution to creating the copyrighted work. (more...)
References
Beresnev, I.A. (2009) The reality of the scaling law of earthquake-source spectra. J. Seism. 13:433-436
Boatwright, J., Choy, G.L. (1986) Teleseismic estimates of the energy radiated by shallow earthquakes. J. Geophys. Res. 91:2095–2112
Bormann, P., Baumbach, M., Bock, M., Grosser, H., Choy, G.L., Boatwright, J. (2002) Seismic sources and source parameters. In: Bormann, P. (Ed.), in: IASPEI New Manual Seismological Observatory Practice, GeoForschungsZentrum Potsdam, Vol. 1, Chapter 3, 94 pp.
Bormann P, Liu, R., Xu., Z., Ren, K., Zhang, L., Wendt, S (2009) First application of the new IASPEI teleseismic magnitude standards to data of the China National Seismographic Network. Bull. Seism. Soc. Am. 99(3):1868-1891
Bormann, P., Saul, J. (2009) Earthquake Magnitude. Ency. Complex. Appl. Syst. Sci., 3, pp. 2473–2496
Bormann, P., Giacomo, D.D. (2010) The moment magnitude Mw and the energy magnitude Me: Common roots and differences, J. Seismol. 15:411–427
Bormann, P. (2020) Earthquake Magnitude. Encyclopedia of Solid Earth Geophysics, Encycl. Ea. Sci. Ser.
Carroll, R.J., Ruppert, D. (1996) The use and misuse of orthogonal regression estimation in linear errors-in-variables models. The Amer. Statis. 50(1):1–6
Choy, G.L., Boatwright, J. (1995) Global patterns of radiated seismic energy and apparent stress. J. Geophys. Res. 100:18205–18228
Choy, G.L., Kirby, S. (2004) Apparent stress, fault maturity and seismic hazard for normal-fault earthquakes at subduction zones. Geophys. J. Int. 159:991–1012
Castellaro, S., Mulargia, F., Kagan, Y.Y. (2006) Regression problems for magnitudes. Geophys. J. Int. 165:913-930
Das, R., Wason, H.R. (2010) Comment on "A homogenous and complete earthquake catalog for Northeast India and the adjoining region" by Yadav, R.B.S., Bormann, P., Rastogi, B.K., Das, M.C., Chopra, S., Seism. Res. Lett. 81(2):232-234
Das, R., Wason, H.R., Sharma, M.L. (2011) Global regression relations for conversion of surface wave and body wave magnitudes to moment magnitude. Natu. Haza. 59(2):801-810
Das, R., Wason, H.R., Sharma, M.L. (2012) Magnitude conversion to unified moment magnitude using orthogonal regression. Jour. Asi. Ear. Sci. 50(2):44-51
Das, R., Wason, H.R., Sharma, M.L. (2013) General Orthogonal Regression Relations between body wave and moment magnitudes, Seismol. Res. Lett. 84:219-224
Das, R., Wason, H.R., Sharma, M.L. (2014) Unbiased Estimation of Moment Magnitude from Body and Surface Wave Magnitude. Bull. Seism. Soc. Am. 104(4):1802-1811
Das, R., Wason, H.R., Gonzalez, G., Sharma, M.L., Choudhury, D., Narayan., R., Pablo, S. (2018) Earthquake Magnitude Conversion Problem. Bull. Seism. Soc. Am. 108(4):1995-2007
Das, R., Sharma, M.L., Wason, H.R., Choudhury, D., Gonzalez, G. (2019) A seismic moment magnitude scale. Bull. Seism. Soc. Am. 109(4):1542-1555
Fuller, W.A. (1987) Measurement Error Models. Wiley, New York, USA.
Giacomo, D, Parolai, D.S., Bormann, P., Grosser, H., Saul, J., Wang, R., Zschau, J. (2010) Suitability of rapid energy magnitude estimations for emergency response purposes. Geophys. J. Int. 180:361-374
Giacomo, D. (2011) Determination of the energy magnitude ME: application to rapid response purposes and insights to regional/local variabilities. University of Potsdam, Germany
Giacomo, D., Bondár, D.I., Storchak, D.A., Engdahl, E.R., Bormann, P., Harris, J. (2015) ISC-GEM: Global Instrumental Earthquake Catalogue (1900–2009): III. Recomputed Ms and mb, proxy Mw, final magnitude composition and completeness assessment. Phys. Earth Planet. In. 239:33–47
Gutenberg, B. (1945a) Amplitude of surface waves and magnitude of shallow earthquakes. Bull. Seism. Soc. Am. 35:3–12
Gutenberg, B. (1945b) Amplitudes of P, PP and S and magnitudes of shallow earthquakes. Bull. Seism. Soc. Am. 35:57-69
Gutenberg, B., Richter, C.F. (1956) Earthquake magnitude, intensity, energy, and acceleration (second paper). Bull. Seism. Soc. Am. 46(2):105–145
Hanks, T.C., Kanamori, H. (1979) A moment magnitude scale. J. Geophys. Res. 84:2348-2350
IASPEI (2013) Summary of Magnitude Working Group Recomms. on Standard Procedures for Determining Earthquake Magnitudes from Digital Data; www.iaspei.org/ commissions/CSOI/Summary_of_WG_recommendations.pdf
Kanamori, H. (1977) The energy release in great earthquakes. J. Geophys. Res. 82:2981-2987
Kendall, M.G., Stuart, A. (1979) The Advanced Theory of Statistics. Vol. 24th ed. Griffin, London, United Kingdom
Kummel, C.H. (1879) Reduction of Observed Equations Which Contain More Than One Observed Quantity. The Analyst 6:97-105
Lindley (1947) Regression lines and the linear functional relation. J. Roy. Statist. Soc. Suppl. 9:218-244
Madansky, A. (1959) The fitting of straight lines when both variables are subject to error. The Amer. Statis. 54(285):173-205
Nath, S.K., Thingbaijam, K.K.S. (2010) Comment on "Estimation of seismicity parameters for India". Seism. Res. Lett. 81:1001-1003
Petrova, N.V., Gabsatarova, P.I. (2019) Depth corrections to surface-wave magnitudes for intermediate and deep earthquakes in the regions of North Eurasia. J. Seismo. 24:203–219
Press, W.H., Teukolsky, S.A., Vetterling, W.T. (1992) Numerical Recipes in C: The Art of Scientific Computing. Cambridge University Press, United Kingdom
Pearson, K. (1901) On Lines and Planes of Closest Fit to systems of Points in Space. Philos. Mag. 2:559-572
Richter, C.F. (1935) An instrumental earthquake magnitude scale. Bull. Seism. Soc. Am. 25(1):1-32
Ristau, J. (2009) Comparison of magnitude estimates for New Zealand earthquakes: moment magnitude, local magnitude, and teleseismic body-wave magnitude. Bull. Seism. Soc. Am. 99(3):1841-1852
Scordilis, E.M. (2006) Empirical global relations converting MS and mb to moment magnitude. J. Seism. 10:225-236
Stefanski, L.A. (2000) Measurement Error Models. Amer. Statist. Assoc. 95:452:1353-1358
Stein, S., Okal, E. (2005) Speed and size of the Sumatra earthquake. Nature 434:581–582
Stromeyer, D., Grünthal, G., Wahlström, R. (2004) Chi-square regression for seismic strength parameter relations, and their uncertainties, with application to an Mw based earthquake catalogue for central, northern and northwestern Europe. J. Seism. 8:143-153
Thingbaijam, K.K.S., Nath, S.K., Yadav, A., Raj, A., Walling, M.Y., Mohanty, W.K. (2008) Recent seismicity in Northeast India and its adjoining region. J. Seism. 12:107-123
Utsu, T. (2002) Relations between magnitude scales. In: International Handbook of Earthquake and Engineering Seismology, Part A, W. H. K. Lee, H. Kanamori, P. C .Jennings and C. Kisslinger (Eds.). Academic Press, Amsterdam, the Netherlands, 81(A):733-746
Vanek, J., Zatopek, A., Karnik, V., Kondorskaya, N.V., Riznichenko, Y.V., Savarensky, E.F., Soloviev, S.L., Shebalin, N.V. (1962) Standardization of magnitude scales. Bull. Acad. Sci. USSR Geophys Ser. 108-111
Wason, H.R., Das, R., Sharma, M.L. (2012) Magnitude conversion problem using general orthogonal regression. Geophys. J. Int. 190(2):1091-1096
Yadav, R.B.S., Bormann, P., Rastogi, B.K., Das, M.C., Chopra, S. (2009) A homogeneous and complete earthquake catalog for northeast India and the adjoining region. Seismol. Res. Lett. 80(4):609-627.