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127
                           (5)  euny  poneL,  ABpp-OM
          Waveform
                                                             (s)  ews  joawsy  ABpp-omy
                                                                                        Signal-to-noise  ratio.
                      Trace


                                                        Seismic  Trace

                                                                                          Events




                                                                                a  low-
                 Alt)
                                                   A(t)
                      Selsmic




                                                                                          Input  seismic  signal.  b)
                                                                                three-layer  model  with
          Seismic


                           i


                          +
                                                                                        5.29

                                                        Noise
                                                 —
                                     Pe
                                                                                  noise.  b)  With  noise.
                                                 >
                                                                                        FIGURE
                                                 z
                          +
                     ss


                                                                                          a)
                                                                                Convolution  of  reflection  coefficients  from
                      ae
                    Reflection
                           i}
                        uh


                [Rew



                                                                                  (Fig.  5.27b).  a)  Without
                                                                                        Traces


                          %
                        ;
                Xk
                                                                                        Seismic
                |






                      Signal
                    Input
                WW)
                                                                                         b
                        |
                                                                                 frequency  input  signal


                                                                                FIGURE 5.28
                      Model
                                 —

                                                                                        Input Signal
                               NihKo PQs
                          =
                          x  SPSS
                a
                                                                                                                           a  mimicking  the  input  signal   c   be   can   Lower Signal  to  High  Signal  to  recognized  on  seismic  trace  with  high   Nolse  Ratio  signal-to-noise  ratio.  c)  Noise  Ratio  On  a  trace  with  low  signal-to-noise  ratio,  seismic  events   within  hidden   are  the  noise.
                    ,  appear   also   inter-   or   signal,   means   the   of                 filter     be   a   has   1976,   which
                  the
         Analysis   reflection   seismic  Other   with   5.5b)   critically  waves,   can   same   attenuate   skip   to   causing   processing   corrections   seismic   acoustic   from   to   scaled   Mathematically,   280   p.   (see   seismic  pro-   (signal-to-   to   enhancing   may  series,   component   components.   al.,   et   trace
         Waveform   seismic   The   5.17).   interfere   groundroll,  Fig.   Direct   source)   point   the   from   best  surveys   have   may   obstructions,   the   in   moveout   input   (resulting   Convolution   signal,   5.28a).   is  series   t   on  changes   of  noise   designed   are   thus   time   each   frequency   (see  Telford   seismic   a
         And    5.8,   5.5c,   processing,   arrivals.   a   from   once   Seismic   Surveys   other   introduced   normal   the   1)   5.28).   seismic   (Fig.   coefficient   time   at   t.   (Fig.  5.28b):   level   the   techniques   reflections,   ,   a   as   other   of  portion
          Processing,   Processing   and   (Figs.   or   as   to  referred   reflected   radiating   5.12a).   than   more   5.19).   continuous.   or  rivers   be   also   poor   or   as  viewed   series   time   (Fig.   input   the   coefficient   A(t)   =   t   time   at   coefficient   time   at   trace   trace  seismic   =A)   N(t)   t.   see  stratigraphic   to   processing   primary   from   Trace   represented   components;   to   Fourier  series   the
          Acquisition,   Acquisition   reflections   acquisition   by   (also   the  across   (energy   (Fig.   reflected   5.18,   5.17,   and   highways,   can   Noise   data.   over-migration   be   can   trace   coefficient   superimposed   with   reflection   reflection   a   with   RC(t)   *   I(t)   signal   input   operator   reflection   seismic   convolved   +   RC(t)]   *   time   at   noise   to  ability  of  reflections,  relative   and   resulting   Seismic   of   trace
          Reflection:   Seismic   primary  image   introduced   waves  Rayleigh   cutting   diffractions   reflections   as   (energy   5.8b,   (Figs.   straight   are   buildings,   recorded   like   seismic   reflection   noise   3)   with   coefficient   the   of   signal   1995):   of  the   convolution   of  the   of  the   the   to   [1(t)   of  the   The   Ratio   amplitude   Acquisition   signals   Components   a   like   sine   of   degree   expressed   be   1995,  Geldart,
          Seismic   by  Induced   to  attempts   phenomena   reflections.   events   and   waves,   time   same   reflections   interfere   lines  survey   with   areas   the   in   factors  through   Trace   A  Convolution   a   2)   with   changes),   reflection   each   polarity   and   input   an   of   Geldart,   =  amplitude   I(t)   *  =   amplitude   =   amplitude   =   A(t)   algebraically   amplitude   =   Noise   to   the   on   5.29).   Fig.   keeping   while   ratio.   P
          Chapter5   Noise   method   or  events,   primary   low-frequency   refracted   the   at   arrive   Multiple   also   face)   when   noise   around   go   bends   or   gaps   data,   of   5.10).   (Fig.   Seismic   convolved   impedance   replacing   amplitude   convolution   Sheriff  and   where:   RC(t)   adds  Noise   where:   N(t)   Signal   depends   files   ratio,   noise   noise   out   signal-to-noise   the   and  Frequency   continuous   A   expressed   certain   c
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