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Borehole seismic data can provide the exact position of the subsurface reflectors at the borehole. Therefore, from borehole data, we can obtain at these locations. can be backpropagated to slowness perturbation using equation (2). In order to integrate the depth control to reflection tomography effectively, we transfer the reflector movement to traveltime perturbation along normal ray, . The traveltime perturbation then is backpropagate to slowness perturbation using following equation:
| |
(7) |

Combining equation (4) and (7), we can obtain a depth controlled reflection tomography (DCRT) scheme:
| |
(8) |

| (9) |

| (10) |

Here, fitting goal (8) and (9) correspond to equation (4) and (7), respectively. Fitting goal 10 is the model styling goal. is a regularization operator. We use a Laplacian as regularization operator for the following application.

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Stanford Exploration Project

10/14/2003