Skip to main content
SpringerLink
Log in

Are new data suggesting a revision of the current M w and M e scaling formulas?

  • Original Article
  • Published:
Journal of Seismology Aims and scope Submit manuscript

Abstract

The paper looks first into the history of the derivation of the currently common formulas for calculating seismic moment magnitude M w and energy magnitude M e into the type of data and relationships available in these years and the parameter assumptions made. The general relationship between M w and M e is analysed and formulated in physical terms. The original M w- and M e-defining relationships are then confronted with equivalent relationships derived on the basis of rich modern magnitude data measured according to recently accepted International Association of Seismology and Physics of the Earth’s Interior (IASPEI) standards for (a) 20-s surface-wave data and (b) broadband body P wave data as well as M 0 and E S data based on digital broadband waveform inversion or integration. The agreement between old and new data and derived relationships is of different quality. The Richter logE S-M S relationship, which has been instrumental for deriving the current standard M w formula, could be very well reproduced with orthogonally regressed M S(20) and logE S data, provided that the latter were not corrected for source mechanism-dependent radiation. In contrast, the relationships between old and modern m B-logE S as well as m B-M S(20) data pairs deviate significantly from the respective Gutenberg and Richter relationships. Also the average E S/M 0 ratio assumed by Kanamori when deriving his M w formula differs from those of respective recent data sets. But the various differences between old and new data and data relationships compensate each other partially when deriving related M w and M e formulas. Therefore, they do not justify the modification of the existing scaling formulas, also for very pragmatic reasons. On the other hand, most striking is the so far not yet considered and by far best correlation that exists between the IASPEI body-wave magnitude standard m B(BB) and seismic energy E S, both estimated via P wave broadband records. The scatter of the logE S-m B(BB) data pair plots is only half of that of logE S-M S(20). This questions the appropriateness of the current exclusive scaling of teleseismic M e to the practically monochromatic long-period 20-s surface-wave magnitude M S. The potential advantage of a complementary M e formula, which scales the currently common teleseismic broadband P wave E S data to P wave broadband m B(BB), as well as the benefit of fast joint determination and interpretation of M w and M e in general, is discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  • Abe K (1975) Reliable estimation of the seismic moment of large earthquakes. J Phys Earth: 381–390

  • Abe K (1981) Magnitudes of large shallow earthquakes from 1904 to 1980. Phys Earth Planet Inter 27:72–92

    Article  Google Scholar 

  • Abe K (1984) Complements to “Magnitudes of large shallow earthquakes from 1904 to 1980”. Phys Earth Planet Inter 34:17–23

    Article  Google Scholar 

  • Boatwright J, Choy GL (1986) Teleseismic estimates of the energy radiated by shallow earthquakes. J Geophys Res 91(B2):2095–2112

    Article  Google Scholar 

  • Bormann P, Dewey JW (2014) The new IASPEI standards for determining magnitudes from digital data and their relation to classical magnitudes (44 pp.; doi: 10.2312/GFZ.NMSOP-2_IS_3.3). In: Bormann P (Ed) 2012; http://nmsop.gfz-potsdam.de

  • Bormann P, Di Giacomo D (2011) The moment magnitude M w and the energy magnitude M e: common roots and differences. J Seismol 15:411–427. doi:10.1007/s10950-010-9219-2

    Article  Google Scholar 

  • Bormann P, Saul J (2008) The new IASPEI standard broadband magnitude m B. Seismol Res Lett 79(5):699–706

    Article  Google Scholar 

  • 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 Seismol Soc Am 99(3):1868–1891. doi:10.1785/0120080010

    Article  Google Scholar 

  • Bormann P, Di Giacomo D, Wendt S (2013) Chapter 3: Seismic sources and source parameters (259 pp.; doi: 10.2312/GFZ.NMSOP-2_ch3). In: P Bormann (Ed) 2012; http://nmsop.gfz-potsdam.de

  • Brune JN, Engen GR (1969) Excitation of mantle Love waves and definition of mantle wave magnitude. Bull Seismol Soc Am 59:923–933

    Google Scholar 

  • Castellaro S, Bormann P (2007) Performance of different regression procedures on the magnitude conversion problem. Bull Seismol Soc Am 97:1167–1175

    Article  Google Scholar 

  • Castellaro S, Mulargia F, Kagan YY (2006) Regression problems for magnitudes. Geophys J Int 165:913–930

    Article  Google Scholar 

  • Choy GL (2011) IS 3.5: Stress conditions inferable from modern magnitudes: development of a model of fault maturity (10 pp., DOI: 10.2312/GFZ.NMSOP-2_IS_3.5). In P Bormann (Ed.), 2012. http://nmsop.gfz-potsdam.de.

  • Choy GL, Boatwright JL (1995) Global patterns of radiated seismic energy and apparent stress. J Geophys Res 100:18,205–18,228

    Article  Google Scholar 

  • Choy GL, Kirby SH (2004) Apparent stress, fault maturity and seismic hazard for normal-fault earthquakes at subduction zones. Geophys J Int 159:991–1012

    Article  Google Scholar 

  • Di Giacomo D, Grosser H, Parolai S, Bormann P, Wang R (2008) Rapid determination of Me for strong to great shallow earthquakes. Geophys Res Lett 35, L10308. doi:10.1929/2008GL033505

    Article  Google Scholar 

  • Di Giacomo D, Parolai S, Bormann P, Grosser H, Saul J, Wang R, Zschau J (2010a) Suitability of rapid energy magnitude estimations for emergency response purposes. Geophys J Int 180:361–374. doi:10.1111/j.1365-246X.2009.04416.x

    Article  Google Scholar 

  • Di Giacomo D, Parolai, Bormann P, Grosser H, Saul J, Wang R, Zschau J (2010b) Erratum to “Suitability of rapid energy magnitude estimations for emergency response purposes”. Geophys J Int 181:1725–1726. doi:10.1111/j.1365-246X.2010.04610.x

    Google Scholar 

  • Di Giacomo D, Bondár I, Storchak DA, Engdahl ER, Bormann P, Harris J (2015) ISC-GEM: Global Instrumental Earthquake Catalogue (1900–2009), III. Re-computed M S and m b , proxy M W , final magnitude composition and completeness assessment, Phys Earth Planet Int 239:33–47. doi:10.1016/j.pepi.2014.06.005

  • Douglas J, Akkar S, Ameri G, Bard PY, Bindi D, Bommer JJ, Bora SS, Cotton F, Derras B, Hermkes M, Kuehn NM, Luzi L, Massa M, Pacor F, Riggelsen C, Sandikkaya MA, Scherbaum F, Stafford PJ, Traversa P (2014) Comparisons among the five ground-motion models developed using RESORCE for the prediction of response spectral accelerations due to earthquakes in Europe and the Middle East. Bull Earthq Eng 12:341–358

    Article  Google Scholar 

  • Dziewonski AM, Chou TA, Woodhouse JH (1981) Determination of earthquake source parameters from waveform data for studies of global and regional seismicity. J Geophys Res 86:2825–2852

    Article  Google Scholar 

  • Edwards B, Fäh D (2013) Measurements of stress parameter and site attenuation from recordings of moderate to large earthquakes in Europe and the Middle East. Geophys J Int 194:1190–1202

    Article  Google Scholar 

  • Edwards B, Allmann B, Fäh D, Clinton J (2010) Automatic computation of moment magnitudes for small earthquakes and the scaling of local to moment magnitude. Geophys J Int 183:407–420

    Article  Google Scholar 

  • Ekström G, Nettles M, Dziewonski AM (2012) The global CMT project 2004–2010: centroid-moment tensors for 13,017 earthquakes. Phys Earth Planet Inter 200–201:1–9

    Article  Google Scholar 

  • Grünthal G, Wahlström R, Stromeyer D (2009) The unified catalogue of earthquakes in central, northern, and northwestern Europe (CENC)-updated and expanded to the last millennium. J Seismology 13:517–541

  • Gutenberg B (1945a) Amplitudes of P PP, and S and magnitude of shallow earthquake. Bull Seismol Soc Am 35:57–69

    Google Scholar 

  • Gutenberg B (1945b) Magnitude determination of deep-focus earthquakes. Bull Seismol Soc Am 35:117–130

    Google Scholar 

  • Gutenberg B (1956) The energy of earthquakes. Q J Geol Soc Lond 112:1–14

    Article  Google Scholar 

  • Gutenberg B, Richter CF (1956) Magnitude and energy of earthquakes. Ann Geofis 9:1–15

    Google Scholar 

  • Hanks TC, Kanamori H (1979) Moment magnitude. J Geophys Res 8:2348–2350

    Article  Google Scholar 

  • IASPEI (2005) Summary of Magnitude Working Group recommendations on standard procedures for determining earthquake magnitudes from digital data, http://www.iaspei.org/commissions/CSOI/summary_of_WG_recommendations_2005.pdf

  • IASPEI, 2013. Summary of Magnitude Working Group recommendations on standard procedures for determining earthquake magnitudes from digital data. http://www.iaspei.org/commissions/CSOI/Summary_WG_recommendations_20130327.pdf

  • Kanamori H (1977) The energy release in great earthquakes. J Geophys Res 82:2981–2987

    Article  Google Scholar 

  • Kanamori H (1983) Magnitude scale and quantification of earthquakes. Tectonophysics 93:185–199

    Article  Google Scholar 

  • Kanamori H, Anderson DL (1975) Theoretical basis of some empirical relations in seismology. Bull Seismol Soc Am 65:1073–1095

    Google Scholar 

  • Kanamori H, Brodsky EE (2004) The physics of earthquakes. Rep Prog Phys 67:1429–1496. doi:10.1088/0034-4885/67/8/R03

    Article  Google Scholar 

  • Kanamori H, Mori, Hauksson E, Heaton TH, Hutton LK, Jones LM (1993) Determination of earthquake energy release and ML using TERRASCOPE. Bull Seismol Soc Am 83(2):330–346

    Google Scholar 

  • Lolli B, Gasperini P, Vannucci G (2014) Empirical conversion between teleseismic magnitudes (mb and Ms) and moment magnitude (Mw) at the Global Euro-Mediterranean and Italian scale. Geophys J Int 199:805–828. doi:10.1093/gji/ggu264

    Article  Google Scholar 

  • McGarr A, Fletcher JB (2002) Mapping apparent stress and energy radiation over fault zones of major earthquakes. Bull Seismol Soc Am 92:1633–1646

    Article  Google Scholar 

  • Newman AV, Okal EA (1998) Teleseismic estimates of radiated seismic energy: the E/M o discriminant for tsunami earthquakes. J Geophys Res 103:26,885–26,897

    Article  Google Scholar 

  • Okal EA, Talandier J (1989) Mm: a variable-period mantle magnitude. J Geophys Res 94:4169–4193

    Article  Google Scholar 

  • Pérez-Campos X, Beroza GC (2001) An apparent mechanism dependence of radiated seismic energy. J Geophys Res 106(B6):11,127–11,136

    Article  Google Scholar 

  • Richter CF (1958) Elementary seismology. W. H. Freeman and Company, San Francisco, viii + 768 pp

    Google Scholar 

  • Schweitzer J, Kværna T (1999) Influence of source radiation patterns on globally observed short-period magnitude estimates (mb). Bull Seismol Soc Am 89(2):342–347

    Google Scholar 

  • Stein S, Okal, EA (2005) Speed and size if the Sumatra earthquake. Nature 434:581–582. doi:10.1038/434581a

  • Storchak DA, Di Giacomo D, Engdahl ER, Harris J, Bondár I, Lee WHK, Bormann P, Villaseñor A (2015). The ISC-GEM Global Instrumental Earthquake Catalogue (1900-2009): Introduction. Phys Earth Planet Int 239: 48–63. doi:10.1016/j.pepi.2014.06.009

  • Stucchi M, Rovida A, Gomez Capera AA, Alexandre P, Camelbeeck T, Demircioglu MB, Gasperini P, Kouskouna V, Musson RMW, Radulian M, Sesetyan K, Vilanova S, Baumont D, Bungum H, Fäh D, Lenhardt W, Makropoulos K, Martinez Solares JM, Scotti O, Živčić M, Albini P, Batllo J, Papaioannou C, Tatevossian R, Locati M, Meletti C, Viganò D, Giardini D (2013) The SHARE European Earthquake Catalogue (sheec) 1000–1899. J Seismol 17:523–544

    Article  Google Scholar 

  • Tsai VC, Nettles M, Ekström G, Dziewonski AM (2005) Multiple CMT source analysis of the 2004 Sumatra earthquake. Geophys Res Lett 32(L17304):1–4

    Google Scholar 

  • Utsu T (2002) Relationships between magnitude scales. In Lee, WHK, Kanamori H, Jennings PC, Kisslinger C (eds.), International Handbook of Earthquake and Engineering Seismology, Part A, Chapter 44:733–746

  • Vanĕk J, Zapotek A, Karnik V, Kondorskaya, NV, Riznichenko YuV, Savarensky, EF, Solov’yov SL, Shebalin NV (1962) Standarizaciya shkaly magnitude (in Russian), Izvestiya Akad SSSR, Ser Geofiz 2:153–158 (with English translation in 1962 by DG Frey, published in Izv Geophys Ser)

  • Vassiliou MS, Kanamori H (1982) The energy release in earthquakes. Bull Seismol Soc Am 72:371–387

    Google Scholar 

  • Wiemer S, Giardini D, Fah D, Deichmann N, Sellami S (2009) Probabilistic seismic hazard assessment of Switzerland: Best estimates and uncertainties. J Seismology 13:449–478

  • Wyss M, Brune JN (1968) Seismic moment, stress, and source dimensions for earthquakes in the California-Nevada region. J Geophys Res 73:4681–4694

Download references

Acknowledgments

The author is grateful to Domenico Di Giacomo for the dataset preparation and the results shown in Figs. 3, 4 and 5 and to Joachim Saul for providing the GFZ m B(BB) values. Comments of D. Di Giacomo on a first draft version also helped to improve the manuscript. Careful reviews and constructive comments by Emile A. Okal and Paolo Gasperini helped to improve the manuscript.

Author information

Authors and Affiliations

  1. Formerly GFZ German Research Centre for Geosciences, Potsdam, Germany

    Peter Bormann

Authors
  1. Peter Bormann
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Peter Bormann.

Additional information

Prof. Peter Bormann passed away on 11 February 2015 when this manuscript had been reviewed with recommendation of minor revisions. The requested revisions were kindly made by Dr. Domenico Di Giacomo, who volunteered for preparing the final version of the paper. The Editor would like to express his sincere thanks to Dr. Domenico Di Giacomo. This is a small tribute to Prof. Bormann’s memory.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bormann, P. Are new data suggesting a revision of the current M w and M e scaling formulas?. J Seismol 19, 989–1002 (2015). https://doi.org/10.1007/s10950-015-9507-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10950-015-9507-y

Keywords

Search

Navigation