Next: Receiver wavefield extrapolation
Up: REFERENCES
Previous: REFERENCES
The recursion in equations (2) and (3) can
be also written in matrix form as
| |
(13) |
where
- W^{+} is a lower bidiagonal matrix containing the downward continuation
operator for all depth levels,
- P^{+} is a column vector containing the source wavefield at all depth
levels, and
- F is a column vector containing the source signature.
Equation (13) represents the downward continuation
recursion written for a given frequency. We can write a similar
relationship for each of the frequencies in the data, and
group them all in a matrix relationship:
| |
(14) |
where
- is a lower bidiagonal matrix containing the downward continuation
operators for all the frequencies in the data,
- is a column vector containing the wavefield data for all
the frequencies, and
- is a column vector containing the source signature for all
the frequencies.
Equation (14) represents the downward continuation
recursion written for a given shot position. We can write a similar
relationship for each of the shot positions in the data, and
group them all in a matrix relationship:
| |
(15) |
where
- is a lower bidiagonal matrix containing the downward continuation
operators for all the shots in the data,
- is a column vector containing the wavefield data for all
the shots, and
- is a column vector containing the source signature for all
the shots.
B
Next: Receiver wavefield extrapolation
Up: REFERENCES
Previous: REFERENCES
Stanford Exploration Project
5/23/2004