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At	  seismic	  discontinuities	  in	  the	  crust	  and	  mantle,	  part	  of	  the	  compressional-­‐wave energy	  converts	  to	  shear	  wave,	  and	  vice	  versa.	  These	  converted	  waves	  have	  been widely	  used	  in	  receiver	  function	  (RF)	  studies	  to	  image	  discontinuity	  structures	  in the	  Earth.	  While	  generally	  successful,	  the	  conventional	  RF	  method	  has	  its	  limitations and	  is	  suited	  mostly	  to	  flat	  or	  gently	  dipping	  structures.	  Among	  the	  efforts	  to overcome	  the	  limitations	  of	  the	  conventional	  RF	  method	  is	  the	  development	  of	  the wave-­‐theory-­‐based,	  passive-­‐source	  reverse-­‐time	  migration	  (PS-­‐RTM)	  for	  imaging complex	  seismic	  discontinuities	  and	  scatters.	  To	  date,	  PS-­‐RTM	  has	  been implemented	  only	  in	  2D	  in	  the	  Cartesian	  coordinate	  for	  local	  problems	  and	  thus	  has limited	  applicability.	  In	  Chapter	  1,	  we	  introduce	  a	  3D	  PS-­‐RTM	  approach	  in	  the spherical	  coordinate,	  which	  is	  better	  suited	  for	  regional-­‐	  and	  global-­‐scale	  seismic imaging.	  	  New	  computational	  procedures	  are	  developed	  to	  reduce	  artifacts	  and enhance	  migrated	  images,	  including	  back-­‐propagating	  the	  main	  arrival	  and	  the	  coda containing	  the	  converted	  waves	  separately,	  using	  a	  modified	  Helmholtz decomposition	  operator	  to	  separate	  the	  P	  and	  S	  modes	  in	  the	  back-­‐propagated wavefields,	  and	  applying	  an	  imaging	  condition	  that	  maintains	  a	  consistent	  polarity for	  a	  given	  velocity	  contrast.	  The	  new	  approach	  allows	  us	  to	  use	  migration	  velocity models	  with	  realistic	  velocity	  discontinuities,	  improving	  accuracy	  of	  the	  migrated images.	  We	  present	  several	  synthetic	  experiments	  to	  demonstrate	  the	  method,	  using regional	  and	  teleseismic	  sources.	  The	  results	  show	  that	  both	  regional	  and teleseismic	  sources	  can	  illuminate	  complex	  structures	  and	  this	  method	  is	  well	  suited for	  imaging	  dipping	  interfaces	  and	  sharp	  lateral	  changes	  in	  discontinuity	  structures.

THREE-DIMENSIONAL PASSIVE‐SOURCE REVERSE TIME MIGRATION OF CONVERT WAVES: A NEW METHOD TO IMAGE THE EARTH’S DISCONTINUITIES