AMO amplitudes

While the kinematics of AMO are independent of its derivation, the amplitude term varies according to the derivation. In the next chapter I present detailed derivations for a true-amplitude function for the AMO operator. In short, the weights are based on the cascade of an amplitude preserving DMO with its asymptotic ``true-inverse'' Chemingui and Biondi (1995). The choice of Zhang-Black's Jacobian yields the following expression for the amplitude term:

$$\begin{eqnarray} \lefteqn{A\left({{\bf \Delta m}},{{\bf h}_{1}},{{\bf h}_{2}},{t... ...er {h_{2}^2\sin^2\Delta \theta}}} \right)}. \EQNLABEL{amo_amp.eq}\end{eqnarray}$$ (4)

The frequency term $\left\vert\omega_2\right\vert$ enters as multiplicative factor in the expression for AMO amplitudes. This term can be applied to the output data in the time domain by cascading a causal half-differentiator with an anti-causal half-differentiator.