### 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) |
---|---|

Pages (from-to) | 1036-1044 |

Number of pages | 9 |

Journal | IEEE Transactions on Signal Processing |

Volume | 45 |

Issue number | 4 |

DOIs | |

State | Published - 1997 |

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### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Signal Processing

### Cite this

**Efficient design of digital filters for 2-d and 3-d depth migration.** / Karam, Lina.

Research output: Contribution to journal › Article

*IEEE Transactions on Signal Processing*, vol. 45, no. 4, pp. 1036-1044. https://doi.org/10.1109/78.564191

}

TY - JOUR

T1 - Efficient design of digital filters for 2-d and 3-d depth migration

AU - Karam, Lina

PY - 1997

Y1 - 1997

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0031126026&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031126026&partnerID=8YFLogxK

U2 - 10.1109/78.564191

DO - 10.1109/78.564191

M3 - Article

VL - 45

SP - 1036

EP - 1044

JO - IEEE Transactions on Signal Processing

JF - IEEE Transactions on Signal Processing

SN - 1053-587X

IS - 4

ER -