Analysis

For convenience, define the following quantities

1.

$\bold H_i(x,y)$: Depth to actual horizon i as a function of x and y.

2.

$\bold H_i^{\prime}(x,y)$: Picked seismic horizon i, defined for all x and y.

3.

$\tilde{\bold H}_i(x,y)$: Updated depth model of i^th horizon.

The path to our final solution has two major steps.

1.

In-Fill and extrapolation of irregular picked seismic horizon

2.

Warping $\bold H_i^{\prime}(x,y)$ to match the well logs