Regularizing seismic inverse problems by model re-parameterization using plane-wave construction

Velocity estimation

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Figure 3. Seismic image from Figure 2 overlaid on top of the interval velocity model estimated by PWC-parameterized Dix inversion.

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Figure 4. Left: migration velocity used for prestack time migration. Right: migration velocity predicted by regularized Dix inversion.

To demonstrate an application of PWC to the seismic velocity estimation problem, we chose a simple Dix inversion formulation (Dix, 1955) applied for interval velocity estimation using the Gulf of Mexico dataset from Figure 1. When Dix inversion is formulated as a regularized estimation problem, the forward operator $\mathbf{L}$ in equations (6) and (7) turns into simple integration (Clapp et al., 1998b; Valenciano et al., 2004). Parameterization by plane-wave construction using the dip field estimated from the image forces the estimated velocity to follow the geological structure.

Figure 3 shows the resultant interval velocity model. Figure 4 shows a comparison between the input and predicted RMS (root-mean-square) migration velocity. We can see that both goals of model estimation are achieved: the estimated model explains the observed data while following a geological structure consistent with the seismic image.

Regularizing seismic inverse problems by model re-parameterization using plane-wave construction