An alternative to these standard approaches is discussed in
Shragge and Sava (2005), who pose seismic imaging directly in
acquisition coordinates and use Riemannian wavefield extrapolation to
propagate wavefields. Initially, a conformal mapping approach was
used to generate structured, locally orthogonal coordinate meshes (see
top panel of figure ). However, the ensuing grid
clustering and rarefaction demanded by orthogonality led to
significant spatial variance in metric tensor
coefficients. Importantly, this variance caused artifacts in the
resulting image, which remains the main drawback of this migration
approach.
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The extension of RWE to non-orthogonal coordinate systems
Shragge (2006) allows for greater flexibility in
coordinate system design. The middle panel in
figure represents a blended coordinate system
that forms the input to the differential mesh algorithm.
Lines predominantly in the horizontal direction mimic topography in
the near-surface and slowly heal to form an evenly sampled wavefield
at depth. The bottom panel shows the coordinate system output
from the gridding algorithm after 15 iterations. Grid
irregularities now heal more rapidly and the mesh becomes very regular
after a few extrapolation steps into the subsurface.