In Cartesian coordinates, the eikonal equation is
where xc=xs or xr are shot or receiver position. Taking partial derivative of both sides of equation (A.1) with respect to xc 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 xc, we have Combining equations (A.2) and (A.3) gives Using the relations between Cartesian coordinates and polar coordinates: we can derive