Dear Colleague,

Standardizing Amplitude Measurements for Magnitude Determinations

Standard magnitude determination is one of the old ongoing problems in observation seismology, especially for monitoring global seismic activity. In this letter I appeal for your support to enable ISC to provide you and the global seismological community, better magnitude assessments and more information about them.

I would also like to draw your attention to the new recommendations made by IASPEI regarding magnitude determinations. The Working Group on Magnitudes (Magnitude WG) of the International Association of Seismology and Physics of the Earth's Interior (IASPEI) Commission on Seismological Observation and Interpretation (CoSOI) was established to recommend standard procedures for taking measurements from digital data to be used in calculating several widely used types of earthquake magnitudes. The recommended procedures from the Working Group have been approved by the IASPEI Commission on Seismological Observation and Interpretation and are expected to be implemented by all seismological centres. The WG is planning to publish an article, in the open literature, that will explain the reasons and arguments that lead to those recommendations.

ISC is preparing to implement the IASPEI recommendations and again your support in providing ISC standard amplitude measurements, as outlined in this document, will be highly appreciated.

Information on current practices

The ISC determinations of mb and Ms, published in the ISC Bulletin in the last several decades, are important and valuable references for quantifying earthquakes strength over a relatively long time span. It is known, however, that the current ISC published magnitudes involve the use of non-standard amplitude measurements. Moreover, relatively few agencies report amplitude measurements and therefore ISC magnitudes are strongly influenced by the measuring practice of few agencies.

We at ISC and users of ISC Bulletin are not sure that we know what amplitudes were reported to us by all agencies or how they are measured. We therefore appeal to all agencies to provide ISC with the following information:

  1. Do you report amplitudes for
    1. P waves?
    2. surface waves?
    3. others? (please specify)
  2. What are the units of the reported amplitude?
  3. Are the reported amplitudes "trace amplitudes" or "ground motions"?
  4. On what part of the seismogram do you measure the required Amax or (A/T)max, e.g.within:
    1. the first few cycles after the phase onset?
    2. a fixed time window of a specified number of seconds after the phase onset?
    3. a flexible time window depending on the length of the P wave train/rupture duration?
    4. within the whole surface wave maximum?
  5. What is the frequency band pass of the instrument or the filtered seismogram?
  6. Is the recording made from a displacement, velocity or acceleration transducer?
  7. What type of instrument response is used (e.g., the actual response of the measuring instrument or a response imitating another seismograph)?
  8. On what component (vertical or horizontal) is the measurement made?
    1. for P waves?
    2. for surface waves?
    3. other waves (please specify)
  9. Do you measure maximum A and the corresponding T or do you measure the maximum (A/T)?
  10. What equations do you use for determining the magnitudes that your institution reports in your bulletin?

Please send us this information at your earliest convenience. ISC will compile the information and post it on the ISC web site.

IASPEI standards of amplitude measurements for magnitude determinations

The attached Appendix presents the magnitude formulae and the standards that the Magnitude WG has recommended and been approved by IASPEI. These standards are defined for determining the magnitudes ML, MS(20), MS(BB), mb , mB, MW and mb(Lg). ISC plans to provide determinations of the magnitude MS(20),MS(BB) , mb, mB and MW. We shall not determine ML and mb(Lg) but rather provide the amplitude values reported to ISC to be used by the community for future developments.

We realize, however, that many agencies will find it important to maintain the procedures they currently use for their magnitudes. Similarly and for the sake of continuity, ISC will continue to determine magnitudes according to the current non-standard practices, allowing different magnitude notation (for example; (mb) and (Ms)). Subject to the availability of data, ISC plans to compute standardized magnitudes MS(20), MS(BB), mb, mB and MW together with the magnitudes (mb) and (Ms). Please note that although MS(20) and (Ms) are expected to be, on average, close to each other, different practices in amplitude measurements will result in different magnitude values for individual earthquakes and specific distance ranges and travel paths.

Reporting Amplitude Measurements

The messages containing current amplitude measurements follow the notation (amplitude measurement codes): A (for any amplitude measure), AML (amplitude for agency's ML),

AMB (Amplitude for estimating (mb)) and AMS (amplitudes for estimating (Ms)).

ISC encourages its data contributors to report seismic moments and amplitudes and periods for determining MS(20),MS(BB), mb, mB and MW as specified by the IASPEI Magnitude WG, along with the amplitudes they currently measure.

We ask you to report the standard amplitudes by using the notation: IAML, IAmb, IAmB, IAmbLg, IAMS20 and IAMSBB where "I" stands for IASPEI, "A" stands for amplitude and the rest stands for the corresponding magnitude convention proposed by the Magnitude WG of CoSOI.

The Magnitude WG is currently monitoring an implementation of the IASPEI standard procedures, to be sure that the procedures as described in the Appendix are consistent with the intent of the WG. Subsequently, the ISC will provide co-operating agencies with a more complete description of the IASPEI standard procedures, including filter parameters that will be necessary to replicate the responses of standard instruments that are specified in the standard procedures.

The Magnitude WG recommendations are also presented on the:

USGS/NEIC ftp site

Updates will be provided on ISC and NEIC websites.

Thank you very much for your continued support and co-operation

Avi Shapira

Director

aviisc.ac.uk

International Seismological Centre
Pipers Lane, Thatcham, RG19 4NS
United Kingdom

Tel: +44 1635 861022
Fax: +44 1635 872358
E-mail: adminisc.ac.uk
www.isc.ac.uk





Appendix:

ML local magnitude consistent with the magnitude of Richter (1935)

For crustal earthquakes in regions with attenuative properties similar to those of Southern California, the standard equation is

(1) ML = log10(A) + 1.11 log10R + 0.00189*R - 2.09

where:

A = maximum trace amplitude in nm that is measured on output from a horizontal-component instrument that is filtered so that the response of the seismograph/filter system replicates that of a Wood-Anderson standard seismograph but with a static magnification of 1;

R = hypocentral distance in km, typically less than 1000 km.

Equation (1) is an expansion of that of Hutton and Boore (1987). The constant term in equation (1), -2.09, is based on an experimentally determined static magnification of the Wood-Anderson of 2080, rather than the theoretical magnification of 2800 that was specified by the seismograph’s manufacturer. The formulation of equation (1) reflects the intent of the Magnitude WG that reported ML amplitude data not be affected by uncertainty in the static magnification of the Wood-Anderson seismograph.

For crustal earthquakes in regions with attenuative properties that are different than those of coastal California, and for measuring magnitudes with vertical-component seismographs, the standard equation is of the form:

(2) ML = log10(A) + C(R) + D

where A and R are as defined in equation (1), except that A may be measured from a vertical-component instrument, and where C(R) and D have been calibrated to adjust for the different regional attenuation and to adjust for any systematic differences between amplitudes measured on horizontal seismographs and those measured on vertical seismographs.



MS(20) teleseismic surface-wave magnitudes at period of ~ 20 sec.

(3) MS(20) = log10(A/T)+ 1.66 log10Δ + 3.3

where:

A = vertical-component ground displacement in µm measured from the maximum trace-amplitude of a surface-wave phase having a period between 18s and 22s on a waveform that has been filtered so that the frequency response of the seismograph/filter system replicates that of a World-Wide Standardized Seismograph Network (WWSSN) long-period seismograph (seismometer period 15s, galvanometer period, 90s);

T = period in seconds (18s ≤ T ≤ 22s);

Δ = epicentral distance in degrees, 20° ≤ Δ ≤ 160°;

and where the earthquake has a focal-depth of less than 60 km.

MS(BB) surface-wave magnitudes from Broad Band instruments.

(4) MS(BB) = log10(A/T)max + 1.66 log10Δ + 3.3

where

(A/T )max = (Vmax/2π ), where Vmax = ground velocity in µm/s associated with the maximum trace-amplitude in the surface-wave train as recorded on vertical-component seismogram that is proportional to velocity, and where the period T, 3s < T < 60s, should be preserved together with A or Vmax in bulletin data-bases;

Δ = epicentral distance in degrees,2° ≤ Δ ≤ 160°, focal depth less than 60 km.


mb short-period body-wave magnitude

(5) mb= log10(A/T) + Q(Δ, h)

where,

A = P-wave ground displacement in µm calculated from the maximum trace- amplitude in the entire P-phase train (time spanned by P, pP, sP, and possibly PcP and their codas, and ending preferably before PP);

T = period in seconds,T < 3s;

A and T are measured on output from a vertical-component instrument that is filtered so that the frequency response of the seismograph/filter system replicates that of a WWSSN short-period seismograph;

Q(Δ, h) = attenuation function for PZ (P-waves recorded on vertical component seismographs) established by Gutenberg and Richter (1956);

Δ = epicentral distance in degrees, 21° ≤ Δ ≤ 100°;

h = focal depth.



mB(BB) broadband body-wave magnitude

(6) mB= log10(A/T)max + Q(Δ,h)

where:

(A/T )max= (Vmax/2π), where Vmax = ground velocity in µm associated with the maximum trace-amplitude in the entire P-phase train (time spanned by P, pP, sP, and possibly PcP and their codas, but ending preferably before PP) as recorded on a vertical-component seismogram that is proportional to velocity in the period-range 0.2s < T < 30s, and where T should be preserved together with A or Vmax in bulletin data-bases;

Q(Δ, h)= attenuation function for PZ established by Gutenberg and Richter (1956), as discussed above with respect to mb;

Δ = epicentral distance in degrees, 21° ≤ Δ ≤ 100°;

h = focal depth.



MW moment magnitude

(7a) MW = (2/3)·(log10M0 - 9.1)

where M0 = scalar moment in N·m, determined from waveform modelling or from the long-period asymptote of spectra.

or its CGS equivalent (M0 in dyne·cm),

(7b) MW= (2/3)·(log10M0 - 16.1)



mb(Lg) regional Lg magnitude measured in a narrow period range around 1s.

(8) mb(Lg) = 5.0 + log10[Ai(10)/110]

where:

Ai(10) = amplitude in µm of "hypothetical" Lg wave at a distance of 10 km, extrapolated from observation at station i.

The extrapolated amplitude Ai(10) is calculated as:

(9) Ai(10) = A(ri)·(ri/10)1/3·[sin(ri/111.1)/sin(10/111.1)]1/2·exp[γ(ri - 10)]

where:

A(Δi) = "sustained ground-motion amplitude" in µm at ithstation, defined as the third largest amplitude in the time window corresponding to group velocities of 3.6 to 3.2 km/s, in the period-range 0.7 to 1.3s.

ri = epicentral distance of ith station, in km.

γ = coefficient of attenuation in km-1. γ is related to the quality factor Q through the equation γ = π/(Q·U·T), where U is group velocity and T is the wave period of the Lg wave. γ is a strong function of crustal structure and should be determined specifically for the region in which the mb(Lg)is to be used.

A and T are measured on output from a vertical-component instrument that is filtered so that the frequency response of the seismograph/filter system replicates that of a WWSSN short-period seismograph. Arrival times with respect to the origin of the seismic disturbance are used, along with epicentral distance, to compute group velocity U.

At the regional and near-teleseismic distances within which mb(Lg) is typically used, equations (8) and (9) may be simplified to:

(10) mb(Lg) = 2.96 + 0.833log10[ri/10] + .4343γri+ log10(Ai)