Subtraction method

Now we have the fitting goals in Equation 15. For the time being, I drop the two regularization terms in Equations 15 and focus my analysis on the data fitting part. For the noise modeling operator ${\bf A_n}$, I computed a 2-D PEF directly from the data (which gives a very approximate coherent noise PEF). The size of this PEF is 25$\times$2. The convolution of the inverse PEF with a panel filled with white noise is shown in Figure . It shows that the PEF predicts both signal (thin lines) and coherent noise (linear event) that will cause crosstalks with the hyperbolic Radon operator. This PEF or coherent noise operator is kept constant during the iterations. I iterated 30 times. Figure displays the model space ${\bf m_s}$ on the left, the modeled noise in the middle (${\bf A_n^{-1}m_n}$), and the residual on the right. As expected, because the PEF is not a perfect coherent noise operator, some signal is trapped in the linear event (middle, Figure ). Figure shows the spectrum of the residual with the ``simplest'' inversion along with the spectrum of the residual for the subtraction scheme.

After 100 iterations of the subtraction scheme, we see (Figure ) that the model space does not vary too much, as opposed to the ``simplest'' approach (Equation 9). This method is stable with respect to the number of iterations.