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In Cartesian coordinates, the eikonal equation is

where *x*_{c}=*x*_{s} or *x*_{r} are shot or receiver position.
Taking partial derivative of both sides of equation (A.1) with respect to *x*_{c}
gives
The right-hand side of the equation is zero because the slowness model is
independent of shot-receiver position.
Assume the derivatives of the traveltimes are continuous functions of (*x*,*z*)
and *x*_{c}, we have
Combining equations (A.2) and (A.3) gives
Using the relations between Cartesian coordinates and polar coordinates:
we can derive

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Stanford Exploration Project

12/18/1997