Abstract
For converted waves, stacking traces with a common reflection point,
forming gathers, and performing dip moveout (DMO) all require accurately
calculating the location of conversion points. Because of the asymmetrical
paths of converted waves, even for horizontally layered media, the
calculation of a conversion point for converted waves is complicated.
Previous authors have obtained analytic solutions for the conversion
point for converted waves in a horizontally layered media. We extend
those results to the more general case of converted waves from a
dipping reflector with a homogeneous, isotropic overburden. By using
Snell's law, we derive a quartic equation and solve it uniquely for
the conversion point. The resultant analytic expression is a function
of offset, compressional-, and shear-wave velocities; normal reflector
depth; and dip angle at the conversion point. This solution can be
readily used to generate accurate synthetic seismic responses for
converted waves based on ray theory. It also can be extended to operators
for stacking converted waves and applying DMO correction.
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