Chapter 4. Magnitude Determinations

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1 Chapter 4. Magnitude Determinations Both the local Richter magnitude (XMAG) and the coda duration magnitude (FMAG) may be computed by HYPOELLIPSE. The computation o these magnitudes is described below. 4.1 Coda duration magnitude, FMAG FMAG is calculated according to an empirical equation (Lee and others, 197; Lahr and others, 1975; Bakun and Lindh, 1977) which can be adjusted to agree with the local Richter magnitude scale. The equation or FMAG is FMAG = C where: +C log ( F * )+C D +C Z +C Chapter 4-1 ( log ( )) 1 10 C * C C 1, C, C 3, C 4, and C 5 are ound empirically and correspond to the RESET TEST variables 31, 3, 33, 40, and 43, respectively (see..4). F = F-P time (s), by USGS convention deined to be the time interval between the arrival o the P phase and the time when the envelope o the coda drops to 1 cm peak-to-peak amplitude on a Teledyne Geotech Model-6585 ilm viewer with 0 x magniication. D = Epicentral distance in km. Z = Hypocentral depth in km. c = Station FMAG correction rom TIME DEPENDENT STATION parameter record (see..5.3) For Caliornia C 1 = or Alaska C 1 = C =.0 C =.0 C 3 = C 3 = 0.0 C 4 = 0.0 C 4 = C 5 = 0.0 C 5 = 0.0 The station correction (c) is not added to the coda magnitude calculated, but is used as a multiplier o the observed coda. Thereore a station with no FMAG correction should have FMAG correction equal to 1.0. I the STATION record has no entry or FMAG F

2 correction, then the correction will be set equal to 1.0. The ith, C 5, term in the ormula can be used to compensate or the nonlinear relationship o log(f) with magnitude (Bakun and Lindh, 1977). I the MAGNITUDE OPTION code is negative then the F minus P coda length (F-P) rom the ARRIVAL TIME record will be converted into the F minus S coda length (F-S) by subtraction o the S-P time. This ormulation may be useul or earthquakes with wide depth variations, but is now only experimental. Coda magnitude will not be computed or a station i the portion o the coda ollowing the S arrival is less than 0% o the total coda duration. This prevents an FMAG rom being computed or stations without a signiicant coda ollowing the S phase. 4. Local Richter magnitude, XMAG 4..1 Equation used to compute Richter magnitude The ormula or computing Richter magnitude is: XMAG = log ( A ) + [- B1+ B logx ] + G X M A G = Log base 10 o maximum zero-to-peak amplitude in mm as recorded on a standard Wood-Anderson seismograph. + Approximation to Richter's loga o rom Eaton (1970), which accounts or amplitude attenuation with distance. See Figure Station Correction X M A G = log(a/) + (-B 1 + B log(x )) + G where: A = Maximum peak-to-peak amplitude in mm For 1 km < D < 00 km B 1 = 0.15 B = 0.80 For 00 km < D < 600 km B 1 = 3.38 B = 1.50 Chapter 4-

3 X = D + Z and D is the epicentral distance and Z the ocal depth in km. G = Station XMAG correction, as speciied on the TIME DEPENDENT STATION parameter record (see..5.3). XMAG is not computed i X is not in the range 0.1 to 1,500 km. Figure 4-1. Comparison o the term log A o rom Richter (1958) (dots) with the approximation (straight lines) used in HYPOELLIPSE. 4.. USGS-style system calibration and XMAG ormulation A system o station calibration has been developed by the USGS that is based on the assumption that the only dierence between the response o stations using the same type o instrumentation is the gain level. On this basis, a series o calibration curves has been developed or use in computing XMAG that only need to be adjusted or an individual station's overall gain. The development o these calibration parameters is summarized below, and ollows the method described by Eaton (1970). Chapter 4-3

4 At any requency, the elements involved in recording ground motion are: Element: Seismometer Response Ground Motion System Response Geophone Signal Telemetry Viewer screen Amplitude peakto-peak h mm E G microvolts(m V) A mm Seismometer Response, R S (), R E G ( ) = microvolts mm S / h System Response, including telemetry and viewer, V(), V A E ( ) = mm / microvolt G Total Harmonic Magniication, MT() MT( )= RS V = A h The system response at some requency may be calculated rom the response at a particular requency p multiplied by the ratio o the response at to the response at p V ( ) V ( ) = V ( p) V ( p) I the viewer amplitude A is measured or input signals E G o constant amplitude and varying requency then the ratio V ( ) V ( p) = A( ) A( p) may be calculated as a unction o requency. Thus V ( ) = V ( p) A( ) A( p) Chapter 4-4

5 V(p) is calculated or p = 5 hz or a 10 µv RMS input signal. 10 µv RMS equals 8.8 µv peak-to-peak. Let the amplitude, A(5), or this signal be deined as the value C10. V ( ) = C A( ) A(5) The ormula or seismometer response is: R S ()= ( F O - π ) 3 G LE + 4 B F O where: F o = natural requency in Hz B = damping constant GLE = motor constant m V/mm/s Thus the total harmonic magniication is: M T ()= R S V = ( F O - π ) 3 G LE + 4 B F O C A() A(5) TGN() is deined to be Rs() divided by 8.8. Using this deinition, the total magniication becomes: A() M T ()= C10 TGN() mm(viewer)/mm(ground) A(5) Total Harmonic Magniicatio n = Station "Gain" * System requency response * Seismometer response divided by 8.8 M T () = C10 * A()/A(5) * TGN() To calculate magnitudes equivalent to the local Richter magnitude it is necessary to calculate the amplitude B() that would have been read on the seismogram rom a Wood- Anderson seismograph. The magniication o the Wood-Anderson is Chapter 4-5

6 M WA ()= ( F O ) + 4 B F O mm(wa record)/mm(ground) with F o = 1.5 and B = 0.8. Urhammer and Collins (1990) ound the static magniication to be 080 rather than 800. For this reason, TEST(5) is provided to adjust this parameter. The amplitude that would be measured on a Wood-Anderson record is: B() = A() M M T () WA () B()= A() * M WA() TGN() A(5) A() / C10 A() (MWA A(5))/(TGN A()) C10 Amplitude (peakto-peak in mm) as measured on viewer. is also measured on viewer. Value is determined by interpolation in the RSPA table corresponding to the system in use. Station calibration rom station record. It is convenient to carry out the interpolation in terms o a response table (RSPA): TGN( n )A( n ) RSPA(n) = log vs log( M WA( )A(5) n n ) where log( n ) = n Using the table o RSPA(n), the ollowing ormula is used to compute XMAG: XMAG = log A C10 - R k + [- B1+ B log X ] + G Log(A/C10) - Rk [-B1 + Blog X] G Log o maximum zero-to-peak amplitude in mm as recorded on a standard Wood-Anderson seismograph where Approximation to Richter's log A o Chapter 4-6 Station Correction

7 Rk = requency response o system number k or requency interpolated rom table o RSPA(n). A = Maximum peak-to-peak amplitude in mm. C10 = USGS peak-to-peak calibration amplitude or 10-m V rms, 5-hz preampliier input. B1 and B were deined above. X = D + Z where D = epicentral distance and Z = ocal depth in km, and G = Station XMAG correction Calibration curves or additional systems For eight systems previously used at the USGS these values are stored in the RSPA table or n = 15 to 34, which corresponds to to Hz or to periods o 3.16 to s. Up to nine additional calibration tables may be used, as described in section..10. Using this option, ive such tables (corresponding to system response codes 9-13) have been deined or use with the USGS A1VCO (Rogers and others, 1980), and are described below. The A1VCO gain is automatically reduced by a actor o 10 or by a actor o 500 when large signals are being recorded. In order to take these gain states into account in computing magnitude, column 6 o the ARRIVAL TIME record (see..6.) contains either a 0, 1, or, corresponding to normal gain, gain reduced by a actor o 10, or gain reduced by a actor o 500. System response code 9 has been assigned to an A1VCO recorded on a Develocorder and viewed with a magniication o 0. M T ( F n ) RSPA(n)=, 10 M WA( F n ) LOG where F n is the requency deined by log(f n ) = n, M T (F n ) is the magniication o an ideal A1VCO at requency F n and gain zero, & M WA (F n ) is the magniication o a Wood-Anderson instrument at requency F n. To account or variations in geophone motor constant, gain setting and other actors between dierent stations, the C10 value is deined to be: N MAMP C10 =, where: PAMP MAMP is the measured peak-to-peak amplitude in mm o the 5-Hz calibration signal, Chapter 4-7

8 PAMP is 49.1 mm, the theoretical peak-to-peak 5-Hz calibration signal level or an ideal A1VCO with Develocorder attenuator setting o, and N is the A1VCO ield gain minus. System response code 10 has been assigned to an A1VCO recorded on FM tape and processed on the USGS CUSP digital playback system. N MAMP C10 =, where: PAMP MAMP is the peak-to-peak amplitude o the 5-Hz calibration signal in counts, measured on a high-gain Siemens playback. PAMP is 60 counts, the theoretical peak-to-peak 5-Hz calibration signal level or an ideal A1VCO played back on the Siemens, and N is the A1VCO ield gain. System response code 11 has been assigned to an A1VCO recorded by the PC system. N MAMP C10 =, where: PAMP MAMP is the peak-to-peak amplitude o the 5-Hz calibration signal in counts, as recorded by the PC, PAMP is 60 counts, the theoretical peak-to-peak 5-Hz calibration signal level or an ideal A1VCO recorded by the PC, and N is the A1VCO ield gain. System response code 1 has been assigned to an A1VCO-Siemens high-gain playback. N MAMP C10 =, where: PAMP MAMP is the amplitude o the 5-Hz calibration signal in mm, measured on a high-gain Siemens playback. PAMP is 18 mm, the theoretical 5-Hz calibration signal level or an ideal A1VCO played back on the Siemens, and N is the A1VCO ield gain. Siemens "ink squirt" playbacks are made at the USGS with one o two gain settings, high or low (reduced by a actor o 4 rom high). In order to take the Siemens playback gain into account in computing magnitude, column 61 o the ARRIVAL TIME record (see..6.) contains either 0 or 1, corresponding to high or low gain, respectively. System response code 13 has been assigned to an A1VCO recorded on the UAGI Masscomp computer system. Chapter 4-8

9 N MAMP C10 =, where PAMP MAMP is the amplitude o the 5-Hz calibration signal ater conversion to millivolts, PAMP is 4000 millivolts, the theoretical 5-Hz calibration signal level or an ideal A1VCO recorded on the Masscomp system, and N is the A1VCO ield gain Magnitude determination when more than one source is possible ARRIVAL TIME records include a code in column 108 (see..6.) that indicates the source o the amplitude measurement. For example, a given station could be recorded simultaneously on a Develocorder and on a computer system. Interpretation o the amplitude will clearly depend upon the data source being used to make the measurements. The TIME-DEPENDENT STATION records (see..5.3) allow up to ive sources to be used simultaneously or a given station. The magnitude subroutine requires that amplitudes read on certain sources have the appropriate response calibration inormation available in the station list in order to compute a magnitude. The source codes used or Alaska data processing are given below. Also shown is the corresponding System Response Code, when a speciic code is required or magnitude calculation. Source Code Response Function V PRIME USGS 0x ilm viewer 1 PRIME USGS 0x one-ilm digitizer 4 PRIME USGS 0x our-ilm digitizer * PRIME Assumed to be USGS 0x ilm H USGS Helicorder 10 USGS FM tape, digitized and processed on CUSP E PRIME USGS FM tape, digitized and processed on Eclipse computer S 1 USGS FM tape played back into Siemens "ink-squirt" L USGS portable RCA/COSMAC ELOG portable digital recorder Chapter 4-9

10 P,O,U,I,G,K 11 AEIC PC digital recorder (PCSEIS) P = Cordova, Petersburg, Yakutat, and Fairbanks O = Fairbanks U = FOCUS I = CALIBRATE G = EVENT Fairbanks K = CODA Fairbanks Z AEIC Spurr Broad-Band Digital PC recorder (PCSEIS) 5 USGS ive-day tape recorder M A SMA1 and SSA strong-motion recorder UAGI 0x ilm % Assumed to be UAGI 0x ilm R UAGI Helicorder D 13 UAGI Masscomp digital data rom DAQ or DAN J 13 Same as D, but measured automatically by JadePost X 13 Same as D, but measured automatically by Xpick F W T B UAGI ilm read by USGS while visiting UAGI Alaska Tsunami Warning Center (ATWC) 0x ilm ATWC teletype, corrected or satellite delay Published bulletin (EDR, ISC. etc) Chapter 4-10

11 C N Q Canadian data rom magnetic tape or digital ormat NEIS, corrected or satellite delay PDAS100 portable digital recorder Y Field data logger such as Quanterra, K, or UNIX box I the amplitude source code on the arrival-time record is blank then the code entered on the BLANK SOURCE option record, which may be any character including a blank (see..3.1), will be used instead. I the amplitude source code is a blank, "V", "1", "4", or "*", then the primary system response unction and the XMAG calibration constant speciied in columns 10-0 o the TIME-DEPENDENT STATION record will be used in computing XMAG. I the amplitude source code is not blank, and either does not appear in the above table or does not have a response unction associated with it, then an XMAG value will not be computed or that amplitude. Otherwise, a C10 value or the systemresponse unction listed in the table above is sought rom the TIME-DEPENDENT STATION records. I the station archive does not have the required C10 value, then XMAG will not be computed or this station UAGI computation o XMAG The University o Alaska Geophysical Institute (UAGI), periodically calibrates each o its seismic stations at a series o periods. These data are maintained in a table that consists o up to 1000 logical records or the SUN version and 100 or the PC version. The data on each record is ordered in the ollowing manner: station_name, source_code, begin_yrmody, end_yrmody, npairs, period(1), sysmag(1), period(), sysmag(),..., period(npairs), sysmag(npairs). Pairs must be in order o increasing period. Item Format Station_name A4 (columns 1-3 or 1-4) Source_code A1 (column 5 or 6) Begin_yrmody o calibration (eg., 88119) End_yrmody o calibration Npairs - number o pairs to ollow Period Free ormat integer Free ormat integer Free ormat integer Free ormat real (s) Chapter 4-11

12 Sysmag - system magniication Free ormat real (counts/mm ground displacement) The name o this ile must be entered on a UOFACAL record included with the input data (see..3.18). Stations with a primary system-response code equal to 18 (in columns o the TIME-DEPENDENT STATION record, see section..5) will have an amplitude magnitude (XMAG) computed only i calibration data or the corresponding time period is ound in the table. To allow or dates ater 1999, years are set to ; years are set to Summary o parameters that control the magnitude calculations The overall preerred magnitude is entered on the SUMMARY record in columns 37-38(see.4.1). This magnitude may be either the average XMAG, average FMAG, or the average o XMAG and FMAG, as determined by the MAGNITUDE OPTION code (see..3.3) FMAG The computed FMAG or each station is entered on the ARCHIVE ARRIVAL TIME record (columns ; see..15) and the average FMAG or the event is entered on the SUMMARY record (columns 7-73; see.4.1). The parameters or the FMAG equation are set by TEST variables 31, 3, 33, 40, and 43. The TIME-DEPENDENT STATION parameter record (see..5.3) includes: FMAG weight, which determines how each station's FMAG is weighted in computing the average FMAG or the earthquake. FMAG correction, a multiplicative correction-actor. The ARRIVAL TIME record (see..6.) includes the measured coda duration (F-P) in seconds and the coda duration source code. The source code is just or documentation and is not used by HYPOELLIPSE XMAG The XMAG or each station is entered on the ARCHIVE ARRIVAL TIME record (columns ; see..15) while the average XMAG or the earthquake is entered on the SUMMARY record (columns 70-71; see.4.1). Chapter 4-1

13 USGS XMAG The TIME DEPENDENT STATION parameter record (see..5.3) may include up to ive system response codes and corresponding calibration constants. This allows magnitude calculations or a station to be based on amplitudes measured on any o ive recording systems. Calibration curves or nominal gain settings may be entered into the program (see..10) The ARRIVAL TIME record (see..6.) includes the maximum peak-to-peak amplitude, the period o maximum amplitude, the A1VCO gain-state, the Siemens playback gain state, and the amplitude source code UAGI XMAG The TIME DEPENDENT STATION parameter record must have system response code 18 speciied (columns 10-11; see..5.3). A table o station calibrations must be speciied with a UOFACAL OPTION record (see 4..3). The ARRIVAL TIME record (see..6.) includes maximum peak-to-peak amplitude, period o maximum amplitude, A1VCO gain-state, and amplitude source code. Chapter 4-13

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