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Let equation
describe the location of a reflector.
First step: calculation of two-way zero-offset travel time in a true model:

Second step: reverse Eiconal's continuation of *t*_{0}(*x*) with wrong
velocity :

| |
(73) |

Third step: imaging from the condition

| |
(74) |

Inserting equation (73) into equation (74) and solving with
respect to *z*, we derive location of the image in depth-section:
The reflection image in time section we receive after substitution is:
Time-to-depth migration in this situation is depth scaling with true velocity
:
We see that depth scaling does not supply correct imaging, although the error is not big: it is proportional to .

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Stanford Exploration Project

1/13/1998