2-­‐2  

i.   Basic  trace  opera-ons  and  resampling    

ii.  Trace  rota-ons  

iii.  Frequency  domain  opera-ons  and  filtering  

Pre-­‐processing  

•  Seismic  data  is  rarely  recorded  in  a  form  where  it  is  directly  (sensibly)  analysable  

•  Instrumental  factors,  long  period  noise,  temperature  varia-ons  and  electronic  interference  all  leave  their  mark  on  seismic  data  (especially  from  field  deployments)  

•  Data  may  be  recorded  at  different  sampling  rates  at  different  sta-ons  in  the  network,  or  at  unnecessarily  high  rates  (genera-ng  unprocessable  amounts  of  data)  

•  Finally,  ALL  real  data  contains  noise  which  masks,  to  some  degree  or  another,  the  signal  of  interest  

•  This  lesson  is  an  overview  of  SAC’s  facili-es  with  dealing  with  these  annoyances  

Basic  clean-­‐up  

•  There  are  several  commands  which  are  run  as  a  pre-­‐processing  step  before  most  other  processing  task  

•  These  are  de-­‐meaning  and  de-­‐trending  data,  and  removing  glitches  like  -ming  chirps  or  tears  

•  This  essen-ally  removes  noise  outside  the  frequency  range  of  the  data  

•  The  commands  for  these  are:  rmean,  rtrend  and  rglitches  

•  They  have  some  op-ons  (especially  rglitches),  but  are  generally  run  well  with  the  default  for  most  data  

Example:  

SAC> rglitches

SAC> rtrend

Resampling  data  

•  A  common  processing  step  is  up/down  sampling  data  

•  This  might  be  for  a  variety  of  reasons  (reduce  file  bloat,  match  other  data)  

•  Primary  command  for  upsampling  is  interpolate  

•  This  uses  ‘Wiggins’  interpola-on  (Wiggins,  BSSA,  1976)  •  Easiest  is  to  specify  a  new  DELTA  •  Note  that  this  can  turn  unevenly  spaced  data  into  evenly  

spaced  (thus  allowing  spectral  analysis,  for  example)  

SAC> help interpolate

SUMMARY: Interpolates evenly or unevenly spaced data to a new sampling rate.

SYNTAX: INTERPOLATE {DELTA v} {EPSILON v} {BEGIN v|OFF} {NPTS n|OFF}

Resampling  data  •  Upsampling  

•  Note  that  no  new  informa-on  is  gained:  an  upsampled  trace  is  just  a  smoother  version  with  more  points  

SAC> interp delta 2

SAC> interp delta 0.05

Downsampling  data  

•  Unlike  upsampling,  downsampling  can  introduce  ar-facts,  through  aliasing  

•  This  can  be  mi-gated  by  pre-­‐filtering  the  data  to  the  target  bandwidth  before  resampling  (an(-­‐aliasing)  

•  This  is  done  by  the  command  decimate  •  Decimate  can  reduce  the  sampling  by  a  

factor  n  between  2-­‐7  

•  Other  factors  can  be  achieved  by  chaining  decimate  commands  

SAC> help decimate

SUMMARY: Decimates (downsamples) data, including an optional anti-aliasing FIR filter.

SYNTAX: DECIMATE {n} {FILTER {ON|OFF}}

Resampling  data  

•  Example:  decima-ng  data  

SAC> r example.sac SAC> lh delta npts b e

FILE: example.sac ----------------- delta = 0.10E-01 npts = 4096 b = 0.0 e = 40.950 SAC> decimate 2; decimate 5 SAC> lh delta npts b e

FILE: example.sac ----------------- delta = 0.10 npts = 410 b = 0.0 e = 40.90

2-­‐2  

i.  Basic  trace  opera-ons  and  resampling    

ii.   Trace  rota-ons  

iii.  Frequency  domain  opera-ons  and  filtering  

Rota-ons  •  Some-mes,  seismograms  are  not  

recorded  in  the  orienta-on  most  convenient  to  a  par-cular  processing  method;  either  by  accident  or  design  

•  However,  with  3-­‐component  sensors  we  (theore-cally)  record  full  vector  displacement  

•  Any  3  orthogonal  components  can  be  rotated  to  form  any  other  3  with  no  loss  of  informa-on;  this  is  equivalent  to  a  frame  of  reference  rota-on    

Radial  –  Transverse  reference  frame  

•  A  common  rota-on  in  global  seismology  is  to  rotate  horizontal  components  to  radial-­‐transverse  reference  frame  

•  The  radial  direc-on  is  in  the  direc-on  of  the  great  circle  path  between  the  earthquake  and  sta-on;  transverse  (or  tangen(al)  is  perpendicular  to  that  

•  This  separates  the  SH  wavefield  from  the  (coupled)  P-­‐SV  wavefield,  making  interpreta-on  of  S-­‐phases  easier  

Rota-ons  in  SAC  

•  Command  to  rotate  SAC  traces  is  rotate  

•  Only  2D  rota-ons  are  available  in  SAC  (but  these  can  be  chained  together)  

•  Rotate  operates  on  pairs  of  traces,  these  must  be  the  same  length,  and  have  the  same  sample  rate  

•  There  are  two  kinds  of  rota-on  …  

SAC> help rotate

SUMMARY: Rotates a pair of data components through an angle.

SYNTAX: ROTATE {TO GCP | TO v | THROUGH v} {NORMAL|REVERSED}

Rotate  THROUGH  

•  With  the  through  op-on,  either  2  horizontal  traces,  or  1  horizontal  and  1  ver-cal  are  rotated  through  X  degrees  clockwise  from  their  current  orienta-on  

•  Rota-ons  require  the  cmpinc  and  cmpaz  headers  to  be  set  (and  modify  them)  

SAC> r SWAV.BHZ SWAV.BHR SAC> lh cmpinc

FILE: SWAV.BHZ -------------- cmpinc = 0.0

FILE: SWAV.BHR -------------- cmpinc = 90.0 SAC> rotate through 30 SAC> lh cmpinc

FILE: SWAV.BHZ -------------- cmpinc = 30.0

FILE: SWAV.BHR -------------- cmpinc = 120.0

DEMO

Rotate  TO  

•  With  the  to  op-on,  horizontal  traces  (only)  are  rotated  to  a  specified  azimuth  (degrees  c’wise  from  North)  …  

•  or  to  the  great  circle  path  azimuth  

•  This  generates  the  radial-­‐transverse  components  

SAC> rotate to 45

SAC> rotate to gcp

DEMO

2-­‐2  

i.  Basic  trace  opera-ons  and  resampling    

ii.  Trace  rota-ons  

iii.   Frequency  domain  opera-ons  and  filtering  

Frequency  domain  for  seismology  

•  Fourier  analysis  represents  a  uniformly  sampled  signal  as  a  weighted  summa-on  of  sine-­‐waves  of  different  frequencies  and  phases  (i.e.,  delays)  

•  Any  signal,  however  complex  (such  as  a  seismic  wave)  can  be  perfectly  represented  by  such  a  summa-on  

•  The  set  of  coefficients  which  describe  the  amplitudes  and  phases  of  the  sine  waves  at  each  frequency  is  called  the  frequency  domain  

•  A  -me  variant  signal  like  a  seismic  trace  can,  in  principle,  be  transferred  to  and  from  the  frequency  domain  losslessly  

•  Many  opera-ons  which  are  complex  or  impossible  in  the  -me  domain  become  trivial  in  the  frequency  domain    

Amplitude  spectra  

•  The  frequency  domain  representa-on  of  a  signal  can  be  used  to  iden-fy  dominant  frequencies  in  a  seismic  trace;  these  might  be  signal,  noise  or  both  

Fast  Fourier  Transforms  

•  The  Fast-­‐Fourier  Transform  (FFT)  allows  rapid  transforma-ons  to  (and  from)  the  frequency  domain.  

•  In  SAC,  the  command  fft  computes  the  FFT  of  the  current  trace(s)  in  memory  

•  This  creates  a  frequency  domain  representa-on  of  the  traces  

•  The  spectra  can  be  plofed  with  the  command  plotsp  

SAC> help fft

SUMMARY: Performs a discrete Fourier transform.

SYNTAX: FFT {WOMEAN|WMEAN} {RLIM|AMPH}

SAC> help plotsp

SUMMARY: Plots spectral data in several different formats.

SYNTAX: PLOTSP {type} {mode}

plotsp  

•  By  default  plotsp  plots  the  amplitude  spectrum  and  the  phase,  using  logarithmic  scales,  however  ogen  just  interested  in  the  amplitude  spectrum:  

 plots  the  amplitude  spectrum  only,  using  linear  scales  for  both  axes  

SAC> plotsp am linlin

Reading  and  wri-ng  spectral  files  

•  Once  FFT  has  been  run  on  a  trace,  it  is  converted  to  a  SAC  spectral  file.  This  can  be  saved  and  read  using  the  normal  SAC  read/write  commands.    

•  However,  the  amplitude  or  phase  part  of  a  spectral  file  can  also  be  wrifen  out  as  a  normal  SAC  file,  using  the  writesp  command:  

•  will  write  out  two  normal  SAC  files,  one  called  myfile.sac.AM  containing  the  amplitude  data,  and  one  called  myfile.sac.PH  containing  the  phase  data  

•  This  can  be  useful  for  handling  or  plohng  spectral  data  in  a  way  not  normally  allowed  in  SAC  

•  The  readsp  command  can  be  used  to  create  a  spectral  file  from  two  normal  SAC  files  

SAC> writesp myfile.sac

Filtering  

•  If,  using  spectral  analysis,  we  can  determine  what  frequencies  present  in  our  seismogram  represent  noise,  and  which  signal,  we  can  filter  out  unwanted  frequencies  to  improve  our  observa-on  of  the  phases  we  are  interested  in.  

•  Filtering  covers  a  very  broad  range  of  theory  and  methodology  

•  Filtering  involves  convolving  a  filter  spectrum  with  the  seismogram  spectrum  

•  SAC  has  implements  several  filter  spectra  –  most  commonly  employed  is  the  Buferworth  filter:  

 where  f  is  frequency,  fc  is  the  cut-­‐off  frequency,  and  np  is  the  number  of  poles  (essen-ally  the  sharpness  of  the  cut-­‐off)  

Example:  2-­‐pole  low-­‐pass  Buferworth  filter  

Filtering  in  SAC  

•  Main  filter  commands  in  SAC  are  highpass,  lowpass  and  bandpass  

•  The  filter  type,  corner  frequencies,  poles  and  number  passes  (1-­‐2)are  specified,  e.g.:  

 Filters  the  current  trace(s)  with  a  2-­‐pole  Buferworth  filter,  with  corner  frequencies  at  0.02  Hz  (50  seconds)  and  0.1  Hz  (10  seconds)  

SAC> help bandpass

SUMMARY: Applies an IIR bandpass filter.

SYNTAX: BANDPASS {BUTTER|BESSEL|C1|C2} {CORNERS v1 v2} {NPOLES n} {PASSES n} {TRANBW v} {ATTEN v}

SAC> bp bu co 0.02 0.1 n 2 p 2

Tes-ng  the  response  func-on  of  a  filter  

•  To  test  what  the  amplitude  spectra  of  a  filter  looks  like:  SAC> funcgen impulse delta 0.05 npts 4096 SAC> bp bu co 0.02 0.1 n 2 p 2 SAC> fft (10.6e)FFT default change: not removing the mean DC level after DFT is 0.10802E-04 SAC> plotsp am loglin

Shortcut  is  the  filterdesign  command  …  

SAC> fd bp bu co 5 25 n 2 p 2 delta 0.01 Note: Phase and group delays for single pass.