Automatic determination of depth phases and earthquake focal depth using Cepstral Stacking Method (CSM) and
Standing Order of Data (SOD)
Recep [email protected]
Lingsen [email protected]
Michel [email protected]
Chin-Wu [email protected]
EarthScope USArrayData Processing andAnalysis Short Course
Student ProjectAugust 29, 2010Northwestern University, Evanston-Chicago
Objectives
• Create an automatic process to detect depth phases (pP and /or sP) and determine focal depth
• Report focal depth additional to ones from USGS/IRIS/CMT/regional networks• Report depth phases additional to ISC and
regional network bulletins
Focal depth calculation Depths from pP and sP delay times
)()(
.2)(
spPsP
pppP
htt
htt
h = source depth η = slowness
21
22
21
22
1
1
v
v
s
p
)(
,)sin(
angleofftakeangleincidenceid
dtiparameterRayv
velocitywaveS
velocitywaveP
SP
PsP
P
PpP
tth
tth
)(
2
)(
pPsP
P
Focal Depth
Surface of the Earth
Earthquake Depth= h
h
Alexander and Cakir, 2010
and 1010 11)()()( * titititi beaebeaeFFP
)](cos[]cos[2]cos[2)1()()( 011022* ttabwtbtabaFF
Then
IFTFFtttabttbttatbauC )()()()(2)(2)()1()( *
101022
or
IFTttabtbtabaFF
uC
)](cos[]cos[2]cos[2)]1log[()]}()({log[
)(
01022*
Cepstral Method)()()()( 10 ttbfttaftfts
101)()( titi beaeFtsFT
S(t)=Observed eartquake signal
a and b= amplitude and polarity of delayed signals
Alexander and Cakir, 2010
P
P wave
pP +
pP wave
=
pP-P delay time
Seismic signal
PpP
Time (second)
.
.
.
.
.
.
C1(u)Subwindow
C1(t)C2(t)
C3(t)C4(t)
C1(u)+ C2(u)+ C3(u)
Alexander and Cakir, 2010
Stacking by summing
the subwindows
Stacking by multiplying
the subwindows
Cepstral Stacking Method (CSM)
Alexander and Cakir, 2010
Select Total Window Length (S – P Maximum)
Select Start Time (P onset)Select Subwindow Length Select Percentage Overlap
Calculate Cepstrum of ith Subwindow Product and/or Sum Stack Subwindow Cepstra (i= 1, N)
Pick (non-zero) Delay Time(s) of Largest Cepstral Stack Peak(s)
Select Known or Assumed Crustal Velocity Model for StationCalculate Source Depth from Delay Time of First Large Peak (pP – P)
Calculate Source Depth from Second Large Peak (sP – P)Assign Final Source Depth from One or Both Depth Estimates
CSM data processing workflow (in SAC)
Alexander and Cakir, 2010
AUTOMATIC PROCESSING
INITIALIZE PARAMETERS
Sub-Window Length (sec) Percentage Overlap (%) Stacking (product, sum, both) Multiple Station Stacking (Y/N) Display (all/final sub-stack plots) Automatic Depth Estimation (Y/N)
PROCESS Station k (k=1,M)STACK STATION CEPSTRA
FINAL DEPTH ESTIMATE
Master script (Matlab)SOD
Download earthquake catalog and waveform data
SOD recipe
Matlab master script
Conclusion• Rapid, automatic detection of depth phases
and focal depth• Integrate programming of SOD, Matlab, and
SAC
Discussion• Estimation of focal mechanism• Comparison with theoretical travel time
prediction• Quality control system• Array processing enhances precision
References
• Alexander, S.S. and Cakir, R. (2010) Further Development of the Cepstral Stacking Method (CSM) for Accurate Determinations of Focal Depths for Earthquakes and Explosions., Seismo. Res. Let., 81, 2, p356, 2010.
• SOD manuals - http://www.seis.sc.edu/sod/ • Matlab manuals - http://www.mathworks.com/ • SAC manuals -
http://www.iris.edu/software/sac/manual.html
