For convenience, define the following quantities

- 1.
- : Depth to actual horizon
*i*as a function of*x*and*y*. - 2.
- : Picked seismic horizon
*i*, defined for all*x*and*y*. - 3.
- : 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 to match the well logs

7/5/1998