Fast time-to-depth conversion and interval velocity estimation in the case of weak lateral variations |

We first test the proposed method using a synthetic model with known analytical time-to-depth conversion solutions. In this model, the exact velocity squared is given by

where , which gives a maximum of 25 changes in lateral velocity along the 7 lateral extent of the model. The analytical solutions to time-to-depth conversion in this particular type of model were presented by Li and Fomel (2015). Figure 3 shows the true interval velocity of the model (equation 22), and the analytical and overlaid by the contours indicating image rays and propagating image wavefront. Other inputs for the proposed conversion method are shown in Figure 4. We choose the reference background to be the central trace of the reference , which is constant in this case. The estimated results are shown in Figure 5 and their corresponding errors in comparison with the analytical values are shown in Figure 6. The errors appear to be generally small indicating a good accuracy for all estimated parameters but increase closer to the edges of the model, which are further away from the chosen reference .

model-slow
The true velocity squared (top) of the linear sloth model (equation 22). Analytical
(middle) is overlaid by image rays. Analytical
(bottom) is overlaid by contours showing propagating image wavefront.
Figure 3. |
---|

input-slow
Inputs of the proposed time-to-depth conversion for the linear gradient model. The last input
(not shown here) is taken to be the central trace of
(top) in this case.
Figure 4. |
---|

estcompare-slow
The estimated values of
,
,
in the linear sloth model (equation 22).
Figure 5. |
---|

errcompare-slow
The errors of the estimated values of
,
,
in comparison with the true values in the linear sloth model (equation 22). The errors are small for all estimated parameters indicating a good accuracy of the proposed method.
Figure 6. |
---|

Fast time-to-depth conversion and interval velocity estimation in the case of weak lateral variations |

2018-11-16