A numerical tour of wave propagation |

According to the previous section, it follows that

(99) |

The convolution guarantees

(100) |

Then, Eq. (71) becomes

(101) |

where is a time-reversal wavefield produced using the residual as the source. It follows from reciprocity theorem

(102) |

satisfying

(103) |

It is noteworthy that an input and the system impulse response function are exchangeable in convolution. That is to say, we can use the system impulse response function as the input, the input as the impulse response function, leading to the same output. In the seismic modeling and acquisition process, the same seismogram can be obtained when we shot at the receiver position when recording the seismic data at the position .

A numerical tour of wave propagation |

2021-08-31