Page 146 - Whole Earth Geophysics An Introductory Textbook For Geologists And Geophysicists
P. 146

129

        —
                                                             Spectrum
        Waveform
        Seismic
                                                             Phase

                                                             Spectrum
                                                             Frequency

                                  Pa  BRAS  ge  Nea  SAP  SR
                                                                   bo
           be   Phase   a) Zero   of Event   Time   ------   =   Hz   - 50   10   Spectrum   Phase  Spectrum  Frequency         i   Fo   :   :   epnuydiuy  to   10   at                      5.30b),              os   8   8   8   8   <<   8   °   8   &   &   &€   @   8   coeffi-   (Hz)  Frequency   (Hz) ~   and  Frequency   in   oer  er   ata  only  Phase  Minimum   b)   their   .....---  of  Event  7ime   as   Hz   - 50   10   fre-   tee  SEOs  ae   @pnujdiny                         &
                               us
                                                              give
                                                          shows
                                                                are
                                                            their
       Analysis   can   trace   given   of  a   help   can   example,   For   from   between   exactly   Fig.   reflection   troughs   being   that   that   of   the   5.31a   exactly   at   to   components             Amplitude   Hz  pulse;  frequencies  below   pulse   =   t  larger  positive  and negative
       Waveform   the   of   (2nnt/T)   shift   signal   traces,   frequencies   components   phase   in   in   (“1"   the   alternating   components   spectra   show   and   peaks   Fig.   are   constructively   the           1   Hz,  zero-phase   2. At  about  peak.
       And   expansion   ‘   phase   and   input   the   seismic   has   wave   amplitudes,   the  event   polarity   of   are   frequency   5.30b).   represented,   the  central   one  another.   components   together   5.31b),   “0.1   b   7   10 -50   a   10-50   a  central  negative  sidelobes.  3.  At
      Processing,   series   S  b, sin   +   n=l   t   time   at   amplitude   of   on  events   Fig.  5.22d   that   sine   the   equal   of   time   the   on   there   different   in   Fig.  pulses.  The  frequency   are   Hz)   how   to  relative   frequency   adding   pulse   (Fig.   per  second  constitute   lines)  of  a   to  give   sidelobes.
      Acquisition,   Fourier   a   (2ant/T)   trace  seismic   the  express   wave  components   reflected   in  depicted   expresses   added   with   Near   the   depending   “lobe”  central   the   from   “3”   and   (“2”   Hz   (or  second   spectra  reveal   line   up   of   the   thus  event,   minimum-phase   to  50  cycles  Frequency  components  (thin   together   minima,  giving   the
      Reflection:   T,  time   to   a,cos   5)   n=0   the   of   that   component.   sine   the   of   pulse   simply   be   can   5.30b).   (Fig.   trough,   or   this   from   resulting   times   10-50   two   cycles   per   phase   The   pulse   each   each  pulse,   the   of   time   the   10   from   frequency  components  add   to  to  varying  degrees,  producing  other  (but  smaller)



      Seismic   0   time   =   A(t)   amplitude   coefficients   frequency   of   appearance   zero-phase   series   5.30a)   event   peak   Away   various   at   illustrates   50   t   equal.   for   the   at   For   SHLRSLRIRSSSER   Frequency  (Hz)   frequencies   zero  amplitude.  b)   frequency  components  add

                        =   =    the   the   Fourier   (Fig.   the   5.26).   “sidelobes,”   10   are   components   zero-phase   lobe.   0),  the
          from   as:    A(t)   a,,b,   Visualization   that   Hz   of   central   of  phase   5.31   of   a   amplitude   waves  with   =   (t
      ChapterS   extends   expressed   where:   understand   assume   Hz. The   50   and   the   time   a   is   there   (Fig.   cient   or  peaks,   out   and   Fig.   frequencies   amplitudes   quency   for   that,   peak   central   the   a)  Sine   have   Hz   event   individual   components  add



      148                            50   10                                                             S.30   above  50   of  the   time

                                                                                                        FIGURE   Hz  and   10   L.At   the   —0.015  s,  the   times,  the   RRR ree
   141   142   143   144   145   146   147   148   149   150   151