### Abstract

Two- and three-dimensional (2-D and 3-D) depth migration can be performed using 1-D and 2-D extrapolation digital filters, respectively. The depth extrapolation is done, one frequency at a time, by convolving the seismic wavefield with a complex-valued, frequency- and velocity-dependent, digital filter. This process requires the design of a complete set of extrapolation filters: one filter for each possible frequency-velocity pair. Instead of independently designing the frequency- and velocity-dependent filters, an efficient procedure is introduced for designing a complete set of 1-D and 2-D extrapolation filters using transformations. The problem of designing a desired set of migration filters is thus reduced to the design of a single 1-D filter, which is then mapped to produce all the desired 1D or 2-D migration filters. The new design procedure has the additional advantage that both the 1-D and 2-D migration filters can be realized efficiently and need not have their coefficients precomputed or tabulated.

Original language | English (US) |
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Pages (from-to) | 1036-1044 |

Number of pages | 9 |

Journal | IEEE Transactions on Signal Processing |

Volume | 45 |

Issue number | 4 |

DOIs | |

State | Published - Dec 1 1997 |

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### ASJC Scopus subject areas

- Signal Processing
- Electrical and Electronic Engineering

### Cite this

*IEEE Transactions on Signal Processing*,

*45*(4), 1036-1044. https://doi.org/10.1109/78.564191