Waveequation based seismic migration and inversion tools are widely used by the
energy industry to explore hydrocarbon and mineral resources. By design, most of
these techniques simulate wave propagation in a space domain with the vertical axis
being depth measured from the surface. Vertical depth is popular because it is a
straightforward mapping of the subsurface space. It is, however, not computationally
costeffective because the wavelength changes with local elastic wave velocity, which
in general increases with depth in the Earth. As a result, the sampling per wavelength
also increases with depth. To avoid spatial aliasing in deep fast media, the seismic
wave is oversampled in shallow slow media and therefore increase the total computation cost. This issue is effectively tackled by using the vertical time axis instead of
vertical depth. This is because in a vertical time representation, the "wavelength" is
essentially time period for vertical rays.
This thesis extends the vertical time axis to the pseudodepth axis, which features
distance unit while preserving the properties of the vertical time representation. To
explore the potentials of doing waveequation based imaging in the pseudodepth domain, a Partial Differential Equation (PDE) is derived to describe acoustic wave in
this new domain. This new PDE is inherently anisotropic because the use of a constant vertical velocity to convert between depth and vertical time. Such anisotropy
results in lower reflection coefficients compared with conventional space domain modeling results. This feature is helpful to suppress the low wavenumber artifacts in
reversetime migration images, which are caused by the widely used crosscorrelation imaging condition. This thesis illustrates modeling acoustic waves in both conventional space domain and pseudodepth domain. The numerical tool used to model acoustic waves is built based on the lowrank approximation of Fourier integral operators. To investigate the potential of seismic imaging in the pseudodepth domain, examples of zerooffset migration are implemented in pseudodepth domain and compared with conventional space domain imaging results.
Date of Award  Dec 11 2011 

Original language  English (US) 

Awarding Institution   Physical Science and Engineering


Supervisor  Tariq Ali Alkhalifah (Supervisor) 
