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When the input offset *h*_{1} is parallel to
the output offset *h*_{2},
the determinant of the system eq36
is equal to zero.
In this case,
the 3D AMO operator degenerates to a 2D operator.
The fact that the determinant of the system of equations
is equal to zero means that the two equations are linearly dependent,
and that we are left with only one equation.
However, because the operator is two-dimensional,
the number of components of the unknown also reduces from two to one.
Consequently, another stationary-phase approximation
to the AMO integral need to be solved.
The new equation is quartic and can be solved using Mathematica
to get a solution for the kinematics of the operator.
The resulting expression for the 2D AMO operator is
presented in equation same_azim.eq of the main text.

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** Up:** Derivation of integral AMO
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Stanford Exploration Project

1/18/2001