Electronic Supplement to
The Application of Velocity Spectral Stacking to Extract Information on Source and Path Effects for Small-to-Moderate Earthquakes in Southern Ontario with Evidence for Constant-Width Faulting

by Robert F. Mereu, Savka Dineva, and Gail M. Atkinson

The Determination of Seismic Source Parameters using Two Methods of Analysis

Introduction

A summary of the seismic source parameters computed by two different methods is presented in the Table below. The data in each column was computed as follows:

Data Column

(1) ME is calculated from the total observed S-LG time domain signal energy.

Dineva and Mereu (2009)

(2) ES is the radiated energy in Joules and is computed from ME using the formula

log ES =2 ME + 2.11
(Kanamori et al. 1993)

(Eqn A3 and Figure 13)

Method 1: Parameters calculated from displacement and velocity amplitude spectra
(3) M is computed from Log(MO) where MO is in Newton Meters
M = 2/3 Log(MO) – 6.06
(Hanks and Kanamori, 1979)
(4) MO is calculated from average displacement levels to left of expected corner frequencies.
(5) The stress drop in bars is computed using the formula
Δσ =( 7/16) MO / R3 where Radius R = (2.34 β/ (2π fc)
(Brune 1970, 71)
Method 2: Parameters calculated from the values of Ca, Cb and ME using linear equations presented in the Appendix
(Best estimates of Ca, Cb are determined computed using Total Stack Analysis)
( Ca = − 2/9 and Cb = 1.62 )
The answers obtained represent regional average values for the parameter in question.
Local anomalies may be studied by subtracting Method 2 answers from Method 1 answers.
(6) M is computed from formula M = (2/3-Ca) ME
see Appendix formula A13
(7) MO is computed from log(Mo) = 3/2 M + 9.095
(Hanks and Kanamori, 1979)
(8) Stress Drop (Δσ) is computed using formula
Δσ =(7/16) MO /R3 where R = (2.34 β / (2π fc)
(Brune 1970, 71)
The linear relation between log(Δσ) and ME may also be used
log (Δσ ) = ( 1+3/2 Ca) ME - 0.8217
(Appendix Eqn A11)
(9) The corner frequency (fc) is computed from
log(fc) = Ca Me +Cb
(Eqn A3 and Figure 13)
(10) R (B) = Radius = R = (2.34 β ) / (2π fc) = (0.37 β ) / fc
(Brune 1970,71)
where β = the S wave velocity for region
(11) R (M) = Radius = R = 0.21 β / fc
(Madariaga 1976)
here R = (2.34 β/ (2π fc)
(Brune 1970,71)
The linear relation between log(Δσ) and ME may also be used
log (Δσ ) = ( 1+3/2 Ca) ME - 0.8217
(Appendix Eqn A11)

Table

Table S1. Table of Source Parameters

References

Brune J. (1970). Tectonic stress and spectra of seismic shear waves from earthquakes, Journal of Geophysical Research 75, 4997-5009.

Brune, J. (1971). Tectonic stress and seismic shear waves from earthquakes. Correction, Journal of Geophysical Research 76, 5002.

Dineva, S., and R. Mereu (2009). Energy magnitude: a case study for Southern Ontario/Western Quebec (Canada), Seismological Research Letters 80, 136-148.

Hanks, T. and H. Kanamori (1979). A moment magnitude scale, Journal of Geophysical Research 84, 2348-2350.

Kanamori, H., J. Mori, E. Hauksson, T.K. Hutton, and L. M. Jones (1993). Determination of earthquake energy release and ML using Terrascope, Bulletin of the Seismological Society of America 83, 330- 346.

Madariaga, R. (1976). Dynamics of an expanding circular fault, Bulletin of the Seismological Society of America 66, 639-666.

[ Back ]