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

Land field data example

To first test the proposed method with real data, we adopt a land dataset provided by the National Petroleum Reserve Alaska (NPRA) (Taylor and Zihlman, 1995). We particularly use the data from line 31-81 from the acquisition season of 1981. Despite the long maximum recording time of 6 $s$ of this dataset, it only contains small-offset information with the maximum offset of 5.225 $kft$ , which leads to a high uncertainty in semblance-based velocity analysis.

We first pre-processed the dataset to correct for uneven recording topography, groundroll attenuation, and surface-consistent amplitudes. We subsequently obtain migration velocity using Fowler's DMO (Fowler, 1984) to perform velocity analysis along with DMO simultaneously. The resultant picked migration velocity is shown in Figure 11 with the maximum lateral velocity variation of approximately 16$\%$ . Figure 12 shows the inputs for the proposed time-to-depth conversion method: Dix-inverted migration velocity squared $w_{dr}(x,z)$ and its gradients evaluated in the time-domain coordinates followed by similar Dix conversion. The output interval velocity squared and its difference from the original Dix-inverted velocity squared are shown in Figure 13. This difference is required to honor lateral variation in the migration velocity field.

vpickdmo
Figure 11. Picked migration velocity from Fowler's DMO for the Alaskan dataset. One can observe a lateral variation of velocity across the extent of the model.

input-alaska
Figure 12. The inputs of the proposed conversion method for the Alaskan field data example: Dix-inverted velocity squared $w_{dr}$ and its gradients.

finalvcompare-alaska
Figure 13. The estimated interval $w(x,z)$ from the proposed method (top) and the difference between the Dix-inverted migration velocity and the estimated velocity using the proposed method (bottom) for the Alaskan field data example.

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