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To allow the implementation of the elastic reverse-time migration algorithm
for marine datasets it is necessary to convert the recorded pressure field
into a vector displacement field. Although the two wavefields are related
by a very simple equation (the displacement field is proportional to
the gradient of the pressure field), it is not possible in practice to
directly apply this equation to most real cases. The vertical component of
the gradient cannot be directly computed in the space domain because the
typical marine geometry comprises a single horizontal line of receivers.
However, with very few assumptions it is possible to separate the upcoming
and downgoing components of the wavefield and obtain an operator in the
frequency-horizontal wavenumber domain that can effectively compute
the pressure gradient. Results with synthetic and real data demonstrate
the applicability of the method.

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Stanford Exploration Project

11/18/1997