next up previous print clean
Next: Conclusions Up: Shragge and Sava: Migration Previous: Numerical examples

Discussion and Future Work

The issues below are important for improving the quality of wave-equation migration directly from topography images. In some cases, we discuss ideas not yet implemented, while in others we speculate on directions of future research.
Muting direct arrivals:
We did not mute out the direct arrivals from the shot gathers, which probably introduced artifacts. In principle, a first-arrival mute is fairly easy to implement; however, their non-linear moveout requires introducing more complicated muting functions. In the future, we will eliminate this source of image contamination.
Using improved mapping weighting functions:
We speculate that amplitudes could become more uniform along the reflectors through the use of a better weighting function. The image is currently interpolated to the Cartesian domain using sinc-function operators, where the image points are weighted by the mapping fold. A better weighting function should include the Jacobian of the transformation between the two coordinate systems.
Including dynamic propagation terms:
We have incorporated only the second-order partial differential terms in the phase-screen approximation for extrapolation direction wavenumber, $k_\tau$. Including the remaining two dynamic terms should lead to reflectors of more uniform intensity, since these terms contribute to wavefield amplitudes.
Incorporating multiple reference media:
The above image was generated using one reference medium (i.e., we performed Taylor expansions about a0 and b0). However, in practice many reference media (e.g., velocities) are often used to generate images through the PSPI approach. Noting that the variability of coordinate spacing is significant (and functions a and b thereby), we surmise that the incorporation of multiple reference media is likely necessary to eliminate existing kinematic errors and to improve diffraction focusing.
Implementing a seperate wavefield datuming step:
By extension, we have shown that this procedure works as a datuming procedure. For example, a coordinate system generated by conformal mapping could be used in an upward continuation scheme to establish the wavefield at a uniform level above topography. Standard Cartesian migration technology could then be applied directly to migrate the datumed wavefield.

next up previous print clean
Next: Conclusions Up: Shragge and Sava: Migration Previous: Numerical examples
Stanford Exploration Project