Abstract
Converted-wave processing is more critically dependent on physical
assumptions concerning rock velocities than is pure-mode processing,
because not only moveout but also the offset of the imaged point
itself depend upon the physical parameters of the medium. Hence,
unrealistic assumptions of homogeneity and isotropy are more critical
than for pure-mode propagation, where the image-point offset is determined
geometrically rather than physically. In layered anisotropic media,
an effective velocity ratio gammaeff = gamma22/ gamma0 (where gamma0
= Vpa/Vsa is the ratio of average vertical velocities and gamma2
is the corresponding ratio of short-spread moveout velocities) governs
most of the behavior of the conversion-point offset. These ratios
can be constructed from P-wave and converted-wave data if an approximate
correlation is established between corresponding reflection events.
Acquisition designs based naively on gamma0 instead of gammaeff can
result in suboptimal data collection. Computer programs that implement
algorithms for isotropic homogeneous media can be forced to treat
layered anisotropic media, sometimes with good precision, with the
simple provision of gammaeff as input for a velocity ratio function.
However, simple closed-form expressions permit hyperbolic and posthyperbolic
moveout removal and computation of conversion-point offset without
these restrictive assumptions. In these equations, vertical traveltime
is preferred (over depth) as an independent variable, since the determination
of the depth is imprecise in the presence of polar anisotropy and
may be postponed until later in the flow. If the subsurface has lateral
variability and/or azimuthal anisotropy, then the converted-wave
data are not invariant under the exchange of source and receiver
positions; hence, a split-spread gather may have asymmetric moveout.
Particularly in 3-D surveys, ignoring this diodic feature of the
converted-wave velocity field may lead to imaging errors.
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