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57                                        of                      com-
            traveled   deriva-                   inverse      represented   acoustic   a   material   P-wave,
       Techniques   distance   first   the       the                   different   when   another   reflected   for  cach   time



       Seismic   the   by   taking   by          taking   by   velocity   the   of   example,   For   of   phases:   3.19).   (Fig.   travel


       Source   divided   determined             calculated   determining   arrivals.   materials   density).   boundary   the   four   S-wave   traveling  in  a  homogenous  medium.  a)  The  slope  of

       Controlled   (AT)   time   AT   = aX   be   3.18a):   (Fig.   (3)   AX   lim   ato   1   T22 (x)   _   V   be   thus       1   aT/ax          in   different   Waves   encounter   and   strikes   into   refracted   (dT/dX).  b)  The  slope  of  the  inverse  of  the  velocity.



            elapsed   Slope   also   can   curve   dT   =   —   =   dX   av   dX   can   wave   =   V       useful   thus   for   Reflected   waves   velocity   material   separates   and      the

            the       (X)   time                 of           is   curves   and   when   of  seismic   one   energy   P-wave,   for  wave   derivative   3.17)  is
            is          travel   written:                     slope,       in                                  first
            line      distance                   type                  partitioned   the   refracted
            the   (AX):   the    be              each         or   travel-time   Refracted,   product   traveling   angle,   (AT/AX)   =  Slope  at  distance  X;   Travel-time  curves   is  the   arrivals  (Figure
            of        given   on   can           for   3.18b):         is                            AT/AX   lim   arrival
            slope   time   a   at   point   time   (Fig.      derivative,   on   energy   (the   wave   oblique   S-wave,   =   dT/dX =  4T~0   for  each

            The   that   slope   that   at   travel   velocities   slope   first   point   Critically   impedance   pressional   Slope   3.18   line   P,  S,  and R
              during   The   tive   The   that:   so   The   the   The   any   at   Seismic   an   at   reflected   FIGURE   the   of  the
                                                                    Direct,










            for     to
            fronts   graph.   according   (T).

            wave   increasing  distance   plotted   the  source   time               side   For   the
            Initial  R  waves,  propagating  across   from  each  receiver.  The  elapsed  time  after  the   travel   receiver   refrac-   Earth.   from   surface
            a)   at  from  the  source.  b)  Travel-time   (X)   the   is            plotted   each   in
            3.17   receivers   The  seismic  traces  are   to  the  distance         are   to   downward   the   time   receiver   the
            FIGURE   P,S,and   several   source  is  fired                           receivers   source   within   travel   curve:   the   to   along


                 ...                                                                   the   increasing   depth   the   source
                                      Traces   of   Receivers                        several   from   as   to   arrivals,   travel-time   the   receiver,  measured

                                      Seismic   for  each   the                      from   (X)  distance   plotted   relates   often   R-wave   the   by               from   travel   the   arrival.   R

                 o                         Jt                                        traces   or               to   or
            é   6                  6    f=,                                   \ Dispersion: Ranges   commonly   T       to   source   PS,
             x   5               (X)  =>   5   ——|____|                              seismic   horizontal   is   because   S-wave,   linear,  expressed   the   wave   the   the   of
       Waves   4   _ ff                                                              graph   the   (T)   studies,   P-wave,   is   for   from   velocity

       Seismic   R 'eCe, ive rs   3   tH   Source   4                                travel-time   to   time   reflection   initial   receiver   time   total   X= distance   seismic



       3         fi   P          From  3                                             a   On   according   3.17).  Travel   and   the   a   to   =   T   =   V
       Chapter                   Distance   2                                        -   side,   by   (Fig.   tion   of   each   source   where:



       56                          1


                                   b        (D)  eu  joAeLL  —=
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