Article,
Common reflection point data-stacking for converted waves
Geophysical Prospecting, 36 (7): 671--688 (October 1988)
DOI: 10.1111/j.1365-2478.1988.tb02186.x
Abstract
For converted waves stacking requires a true common reflection point
gather which, in this case, is also a common conversion point (CCP)
gather. We consider converted waves of the PS- and SP-type in a stack
of horizontal layers.The coordinates of the conversion points for
waves of PS- or SP-type, respectively, in a single homogeneous layer
are calculated as a function of the offset, the reflector depth and
the velocity ratio vp/vs. Knowledge of the conversion points enables
us to gather the seismic traces in a common conversion point (CCP)
record. Numerical tests show that the CCP coordinates in a multilayered
medium can be approximated by the equations given for a single layer.
In practical applications, an a priori estimate of vp/vs is required
to obtain the CCP for a given reflector depth. A series expansion
for the traveltime of converted waves as a function of the offset
is presented. Numerical examples have been calculated for several
truncations. For small offsets, a hyperbolic approximation can be
used. For this, the rms velocity of converted waves is defined. A
Dix-type formula, relating the product of the interval velocities
of compressional and shear waves to the rms velocity of the converted
waves, is presented.
