Dynamic estimation of reflectivity by minimum-delay seismic trace decomposition

Dynamic  es+ma+on  of  reflec+vity  by     minimum-­‐delay   seismic  trace  decomposi+on   Milton  J.  Porsani     Centro  de  Pesquisa  em  Geo1sica  e  Geologia  (CPPG/UFBA)  and  Na=onal   Ins=tute  of  Science  and  Technology  of  Petroleum  Geophysics  (INCT-­‐GP/CNPQ).   Bjorn  Ursin     The  Norwegian  University  of  Science  and  Technology,  (NTNU)   Department  of  Petroleum  Engineering  and  Applied  Geophysics   Michelângelo  G.  Silva     Centro  de  Pesquisa  em  Geo1sica  e  Geologia  (CPPG/UFBA)  

Synthe=c  Seismic  Trace  

The convolutional model for the seismic trace

Deconvolution following the Wiener-Levinson approach The convolutional model for the seismic trace

Seismic traces ACF Obtain the WL filter Apply the filter Deconvolved traces

Time-­‐varying  deconvolu+on   In  =me-­‐varying  deconvolu=on  we  compute  and  apply  a   different  filter  for  each  =me  sample.  

From  this  we  use  the  Levinson  (1947)  algorithm  to  compute  the   minimum-­‐phase  inverse  filter  (Robinson,  1967),  

Time-­‐varying  deconvolu+on   A  different  filter  and  output  for  each  =me  sample  

This  can  be  wriWen  

Minimum-­‐delay  seismic  trace  decomposi+on  

The  inverse  of  the  spiking  filter  is  a  minimum-­‐ delay  wavelet  computed  directly  from  

Equa=on  (4)  may  be  wriWen  as  a  lower  triangular  system  of  equa=on  

and  solved  recursively  for  wk(t)  by  using  back-­‐subs=tu=on,  

The  seismic  trace  is  now  expressed  as  a  sum  of  minimum-­‐delay  wavelets  

Time-­‐varying  deconvolu+on  

Minimum-­‐delay  seismic  trace  decomposi+on  

Comparison  

Combining  eq.  (1)  and  (2)  we  obtain  

The  matrix  F  =  GW  is  also  lower  triangular  with  elements  1  on   the  diagonal.  It  is,  however,  different  from  the  iden=ty  matrix,   so  that  the  two  es=mates  of  reflec=vity  are  different.  

Steps of the dynamic reflectivity estimation method

Comparison  of  adap=ve  predic=ve  deconvolu=on  and  dynamic  minimum-­‐delay   reflec=vity  es=ma=on    of  a  shot  gather  

Input  data  

adap=ve  predic=ve     deconvolu=on  

minimum-­‐delay     reflec=vity  es=ma=on  

Average  amplitude  spectrum  of  the  shot  gathers  

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LAND  DATA  PROCESSING  EXAMPLE   Land  seismic  line  from  the  Tacutu  basin,     located  in  the  North-­‐east  of  Brazil  

•  179  shots  recorded  at  4  ms  sampling  interval     •  96  channels  per  shot       •  split-­‐spread  geometry  with  offsets  from  -­‐2,500  m  to   -­‐150  m  and  150  m  to  2,500  m  and  200  m   •  The  distance  between  the  shots  is  200  m,  giving  a  low   CMP  coverage  of  12  fold  

Flowchart  of  the  seismic  data  processing:  

Signal  and  noise  separa=on  using  SVD  filtering.   (a)  input  data,     (b)  output  data  (signal),     (c)  residual  (noise).  

Input  data  and   corresponding  velocity   analysis.  

SVD  filtered  data   and  corresponding   velocity  analysis.  

SEG, 2010

Local  slope  es+ma+on   Deriva=ve  respect  to  t  

Deriva=ve  respect  to  x  

Input  data  in  (a),    ager  SVD  filtering  in  (b),    and  ager  SVD  filtering  followed  by    dynamic  reflec=vity  es=ma=on  in  (c).  

Velocity  analysis  plots  corresponding  to  the  three  gathers  with  matching  (a),  (b),  and  (c).  

Average  amplitude  spectra  

Detail  of  a  common-­‐offset  panel   A  common-­‐offset  panel  at  2050m    

Ager  SVD  filtering  

Ager  SVD  filtering  followed  by   reflec=vity  es=ma=on  

Stacked  sec+ons   Original  data    

Ager  SVD  filtering  only  

Ager  dynamic  reflec=vity     es=ma=on  only  

Stacked  sec+ons   Ager  dynamic  reflec=vity   es=ma=on  followed  by     SVD  filtering    

Ager  SVD  filtering     followed  by  dynamic   reflec=vity  es=ma=on  

Detail  of  the  stacked  sec=ons  

Original  data.  

SVD  filtered  data   only.  

SVD  filtered  data   followed  by   dynamic   reflec=vity   es=ma=on.  

CONCLUSION        

•  A  new  method  for  es=ma=ng  seismic  reflec=vity  by  decomposi=on  of  a   seismic  trace  in  minimum-­‐delay  wavelets.       •  We  have  also  developed  a  data  processing  strategy  for  noise  removal   and  signal  enhancement  by  combining  SVD  filtering  with  reflec=vity   es=ma=on.       •  The  SVD  filtering  removes  noise  and  improves  lateral  con=nuity  while   the  reflec=vity  es=ma=on  increases  the  high-­‐frequency  content  in  the   data  and  improves  ver=cal  resolu=on.    

ACKNOWLEDGEMENTS  

The  authors  wish  to  express  their  gra=tude  to  INCT-­‐GP/ CNPq/MCT,    CAPES,  PETROBRAS,  ANP,  FINEP,  FAPESB  Brazil   for  financial  support.  We  also  thank  the  VISTA  project    and   the  Norwegian  Research  Council  through  the  ROSE  project.