Interferometric imaging condition for wave-equation migration |

Consider a medium whose behavior is completely defined by the acoustic
velocity, i.e. assume that the density
is
constant and the velocity
fluctuates around a homogenized
value
according to the relation

(12) |

Consider the covariance orientation vectors

(13) | |||

(14) | |||

(15) |

defining a coordinate system of arbitrary orientation in space. Let be the covariance range parameters in the directions of , and , respectively.

We define a covariance function

(16) |

(17) |

Given the IID Gaussian noise field
, we obtain the random
noise
according to the relation

(18) |

(19) | |||

(20) |

are Fourier transforms of the covariance function and the noise , denotes Fourier transform, and denotes inverse Fourier transform. The parameter controls the visual pattern of the field, and control the size and orientation of a typical random inhomogeneity.

Interferometric imaging condition for wave-equation migration |

2013-08-29