Earthquake Source Parameters

Earthquake Magnitudes

An Information Sheet (IS 3.3) that discusses the new IASPEI standards for determining earthquake magnitudes from digital data and their relationship to classical magnitudes. The document outlines the need for standardized measurement procedures to ensure consistency and comparability of earthquake magnitude data across different seismic networks and agencies. The aim is to address discrepancies and biases in magnitude measurements, which can arise due to different instruments, calibration methods, and data processing techniques.

Summary of Magnitude Definitions:

1. ML (Local Magnitude):

   • Developed by Richter (1935) for earthquakes in Southern California.

   • Standard equation: ML=log 10(A)+1.11log10(R)+0.00189R−2.09 

   • A is the maximum trace amplitude, and R is the hypocentral distance.

   • Adjustments are made for different regional attenuation and station-specific factors.

2. mB (Medium-period Body-wave Magnitude):

   • Original Gutenberg body-wave magnitude measured on medium-period instruments.

   • IASPEI uses a broadband version (mB_BB) with a period range from 0.2s to 30s.

   • The amplitude is measured as the maximum velocity Vmaxand the magnitude is calculated using 

mB BB=log 10(V max/2π)+Q(Δ,h)−3.0

2. • Applicable for magnitudes down to about 4 or 5.

3. mb (Short-period Body-wave Magnitude):

   • Introduced with the deployment of short-period seismographs (e.g., WWSSN-SP).

   • Calculated using mb=log 10 (A/T)+Q(Δ,h)−3.0.

   • A is the P-wave amplitude, and T is the period of the maximum amplitude.

   • Subject to "magnitude saturation" for larger earthquakes.

4. Ms_20 (Teleseismic Surface-wave Magnitude at 20s):

   • Calculated using Ms 20 =log 10 (A/T)+1.66log 10 Δ+0.3. 

   • A is the vertical-component ground displacement at a period between 18s and 22s.

   • Applied to shallow-focus earthquakes.

5. Ms_BB (Broadband Surface-wave Magnitude):

   • Similar to Ms_20 but applied over a broader period range (3s to 60s).

   • Calculated using Ms BB =log 10 (V max /2π)+1.66log 10 Δ+0.3. 

   • More applicable to a broader range of earthquake types.

6. mb_Lg (Regional Magnitude based on Lg waves):

   • Calculated using mb Lg =log 10 (A)+0.833log 10 [r]+0.4343γ(r−10)−0.87. 

   • A is the sustained ground-motion amplitude in a period range around 1s.

   • r is the epicentral distance, and γ\gammaγ is a region-specific attenuation coefficient.

7. Mw (Moment Magnitude):

   • Calculated using Mw=(log 10 M 0 −9.1)/1.5, where M0​ is the scalar moment.

   • Provides a consistent measure of earthquake size across all magnitudes.

These definitions ensure that magnitude measurements are consistent and comparable across different seismic stations and networks, enhancing the reliability and utility of seismic data for research and hazard assessment.

Summary of the Magnitudes and Scales

The document, titled "Magnitude Scale and Quantification of Earthquakes" by Hiroo Kanamori, provides a comprehensive overview of different earthquake magnitude scales, their development, and the underlying challenges in quantifying earthquakes. Despite the empirical nature and inherent limitations of these scales, they remain fundamental in seismology, particularly for cataloging earthquakes. The document emphasizes the importance of relating older magnitude scales with newer, more quantitative source parameters to maintain continuity and uniformity in earthquake data. It discusses the physical basis for different magnitude scales, including local magnitude (ML), surface-wave magnitude (MS), body-wave magnitude (mB), and moment magnitude (Mw). The paper also explores the relationships between these scales and the energy radiated by earthquakes, ultimately suggesting that moment magnitude provides a useful and uniform scale for quantifying earthquakes across different depths and regions.

List of Magnitude Definitions and Mathematical Relations

1. Local Magnitude (ML)

   • Defined by: Richter (1935)

   • Equation: ML​=log10​(A)+some constant

   • Where AAA is the amplitude of seismic waves.

2. Surface-Wave Magnitude (MS)

   • Defined by: Gutenberg (1945a)

   • Equation: MS​=log10​(AS​)+some constant

   • Where ASA_SAS​ is the amplitude of surface waves with a period of about 20 seconds.

3. Body-Wave Magnitude (mB)

   • Defined by: Gutenberg (1945b)

   • Equation: mB​=log10​(AB​)+some constant

   • Where AB​ is the amplitude of body waves with periods typically ranging from 0.5 to 12 seconds.

4. Moment Magnitude (Mw)

   • Defined by: Kanamori (1977)

   • Equation: Mw​=(log10​(M0​)−16.1​)/1.5

   • Where M0​ is the seismic moment.

   • The relation between seismic moment M0​ and energy E is given by E=(Δσ/2μ)​M0, where Δσ is the stress drop, and μ is the rigidity of the medium.

5. Energy-Magnitude Relation

   • Defined by: Gutenberg and Richter (1956)

   • Equation: log10​(E)=1.5MS​+11.8

   • Where E is the energy radiated by seismic waves.

6. Magnitude of Deep and Intermediate Earthquakes (mu)

   • Defined by: Vassiliou and Kanamori (1982)

   • Equation: log10​(M0​)=2.4mu​+10.1

   • Where M0​ is the seismic moment and ​ mu is the magnitude for deep earthquakes.

These relations form the basis of understanding the size and energy of earthquakes, connecting different types of seismic measurements to a unified scale for practical and research purposes.

References:

• Bormann, P. (2002). New manual of seismological observatory practice. URL: https://gfzpublic.gfz-potsdam.de/pubman/faces/ViewItemOverviewPage.jsp?itemId=item_245421, URL2: https://bib.telegrafenberg.de/publizieren/bibliotheksverlag/nmsop; PDF https://moodle2.units.it/pluginfile.php/294221/mod_resource/content/1/manual_seismological_observatory-2002.pdf

• Bormann, P. (Ed.) (2012). New Manual of Seismological Observatory Practice (NMSOP-2), IASPEI, GFZ German Research Centre for Geosciences, Potsdam; http://nmsop.gfz-potsdam.de; DOI: 10.2312/GFZ.NMSOP-2, urn:nbn:de:kobv:b103-NMSOP-2 

• IS 3.3: The new IASPEI standards for determining magnitudes from digital data and their relation to classical magnitudes (P. Bormann, J. Dewey and IASPEI/CoSOI Working Group on Magnitude Measurement), DOI: 10.2312/GFZ.NMSOP-2_IS_3.3, PDF https://gfzpublic.gfz-potsdam.de/pubman/item/item_816929/component/file_5002173/IS_3.3_rev1.pdf

• Hiroo Kanamori (1983), Magnitude scale and quantification of earthquakes, Tectonophysics,Volume 93, Issues 3–4, 10 April 1983, Pages 185-199, DOI: https://doi.org/10.1016/0040-1951(83)90273-1; (URL: https://www.sciencedirect.com/science/article/abs/pii/0040195183902731) PDF  http://gps-prod-storage.cloud.caltech.edu.s3.amazonaws.com/people_personal_assets/kanamori/HKtect83b.pdf

• Kanamori, H. (1978) Quantification of Earthquakes. Nature, 271, 411-414, DOI: https://doi.org/10.1038/271411a0 ;  PDF  http://gps-prod-storage.cloud.caltech.edu.s3.amazonaws.com/people_personal_assets/kanamori/HKnat78.pdf

• Richter, C. F. (1935). An instrumental earthquake magnitude scale. Bull. Seism. Soc. Am., 25,1-32.

• Gutenberg, B. (1945a). Amplitudes of surface waves and magnitudes of shallow earthquakes. Bull. Seism. Soc. Am., 35, 3-12.

• Gutenberg, B. (1945b). Amplitudes of P, PP, and S and magnitude of shallow earthquakes. Bull. Seism. Soc. Am., 35, 57-69.

• Gutenberg, B. (1945c). Magnitude determination of deep-focus earthquakes. Bull. Seism. Soc.Am., 35, 117-130.

• Gutenberg, B., and Richter, C. F. (1954). Seismicity of the Earth and associated Phenomena. 2nd edition, Princeton University Press, 310 pp.

• Gutenberg, B., and Richter. C. F. (1956a). Magnitude and energy of earthquakes. Annali di Geofisica, 9, 1-15.

• Gutenberg, B. and Richter, C.F. (1956b). Earthquake magnitude, intensity, energy, and acceleration (second paper), Bull. Seism. Soc. Am., 46, p. 105-145.

• Hara, T. (2007a). Measurement of the duration of high-frequency energy radiation and its application to determination of the magnitudes of large shallow earthquakes. Earth Planets Space 59, 227-231.

• Hara, T. (2007b). Magnitude determination using duration of high frequency radiation and displacement amplitude: application to tsunami earthquakes. Earth. Planet Space 59, 561-565.

• Kanamori (1977), H. Kanamori, The energy release in great earthquakes, J. Geophys. Res., 82 (1977), pp. 2981-2987

• T.C. Hanks, H. Kanamori(1979(, A moment magnitude scale, J. Geophys. Res., 84 (1979), pp. 2348-2350

• T.H. Heaton, F. Tajima, A. Wildenstein-Mori (1982), Estimating ground motions using recorded accelerograms, (1982)

• R.B. Herrmann, O.T. Nuttli (1982), Magnitude: the relation of ML to mbLg, Bull. Seismol. Soc. Am., 72 (1982), pp. 389-397

• H. Kanamori (1977), The energy release in great earthquakes, J. Geophys. Res., 82 (1977), pp. 2981-2987

• H. Kanamori, D.L. Anderson (1975), Theoretical basis of some empirical relations in seismology, Bull. Seismol. Soc. Am., 65 (1975), pp. 1073-1095

• H. Kanamori, J.W. Given (1981), Use of long-period surface waves for rapid determination of earthquake-source parameters, Phys. Earth Planet. Inter, 27 (1981), pp. 8-31

• H. Kanamori, P.C. Jennings (1978), Determination of local magnitude, ML, from strong-motion accelerograms, Bull. Seismol. Soc. Am., 68 (1978), pp. 471-485

• H. Kawasumi (1951), Measures of earthquake danger and expectancy of maximum intensity throughout Japan as inferred from the seismic activity in historical times, Bull. Earthquake Res. Inst. Tokyo Univ., 29 (1951), pp. 469-482

• S. Miyamura (1978), Magnitude of earthquakes (I), Lecture Notes, Int. Inst. Seismol. Earthquake Eng, Tokyo (1978), p. 83, No. 11

• S. Noguchi, K. Abe (1977), Earthquake source mechanism and Ms — mb relation, Zisin II, 30 (1977), pp. 487-507, (in Jap., with Engl. abstr.).

• M.S. Vassiliou, H. Kanamori (1982),The energy release in earthquakes, Bull. Seismol. Soc. Am., 72 (1982), pp. 371-387