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Imaging by wavefield extrapolation (WE) is based on recursive
continuation of the wavefields from a given depth level to the next
by means of an extrapolation operator :
| |
(1) |

This recursive relation can also be explicitly written in
matrix form as
or in a more compact notation as:
| |
(2) |

where the vector stands for the recorded data,
for the extrapolated wavefield,
for the extrapolation operator and
for the identity operator.
The wavefield at every depth level
is imaged using an imaging operator :

| |
(3) |

where stands for the image at some depth level.
We can write the same relation in compact matrix form as:
| |
(4) |

where stands for the image, and
stands for the imaging operator which is
applied to the extrapolated wavefield .

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** Up:** Theory of wave-equation MVA
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Stanford Exploration Project

11/11/2002