# Automatic determination of earthquake focal depth (and focal

```Automatic determination of depth phases and earthquake
focal depth using Cepstral Stacking Method (CSM) and
Standing Order of Data (SOD)
Recep Cakir
[email protected]
Lingsen Meng
[email protected]
EarthScope USArray
Data Processing and
Analysis Short Course
Student Project
August 29, 2010
Northwestern University,
Evanston-Chicago
Michel Foundotos
[email protected]
Chin-Wu Chen
[email protected]
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
(t pP  t p )  2h .  p
h = source depth
η = slowness
(t sP  t P )  h ( p  s )
h
 1

 p   2  v2 


1
 1

 s   2  v 2 


1
(t pP  t P )
2 P
(t sP  t P )
h
P S
  P  wave velocity
2
  S  wave velocity
sin(i ) dt

,

d
i  incidenceangle (take off angle)
v  Ray param eter
2
Surface of the Earth
h
Earthquake
Depth= h
Focal
Depth
sP
pP
P
Alexander and Cakir, 2010
Cepstral Method
s(t )  f (t )  af (t  t0 )  bf (t  t1 )
S(t)=Observed eartquake
signal
a and b= amplitude and
polarity of delayed signals
FT s (t )  F ( ) 1  ae it0  be it1
an
d

P( )  F ( ) F * ( ) 1  aeit0  beit1
 1  ae
 it0
 beit1



 F () F * () (1  a 2  b2 )  2a cos[t0 ]  2b cos[wt1 ]  abcos[(t1  t0 )]
Then


C (u)  (1  a 2  b 2 )  (t )  2a  (t  t0 )  2b (t  t1 )  ab  (t  t0  t1 )  F ( ) F * ( )
IFT
or
C (u ) 
{log[F ( ) F * ( )]} log[(1  a 2  b 2 )]  2a cos[t0 ]  2b cos[t1 ]  ab cos[ (t  t0 )]
IFT
Alexander and Cakir, 2010
P
P wave
+
pP
pP wave
=
P
pP
Seismic signal
pP-P
delay
time
Time
(second)
C1(u)
Subwindow
C1(t)
C1(u)+ C2(u)+ C3(u)
C2(t)
C3(t)
C4(t)
.
.
.
.
.
.
Alexander and Cakir, 2010
Cepstral Stacking Method (CSM)
Stacking by
summing
the
subwindows
Stacking by
multiplying
the
subwindows
Alexander and Cakir, 2010
CSM data processing workflow (in SAC)
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 Station
Calculate 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
Alexander and Cakir, 2010
AUTOMATIC PROCESSING
Master script (Matlab)
SOD
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
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
```