What will I do?

The two proposed methods are based on the need to have IID residual components. A typical inverse problem arises when we want to minimize the objective function for the fitting goal  

$${\bf 0} \approx {\bf Hm - d},$$ (2)

where ${\bf m}$ is a mapping of the data (unknown of the inverse problem), ${\bf H}$ an operator and ${\bf d}$ the seismic data. The residual r is defined as the difference between input data d and estimated data ${\bf \tilde{d}=Hm}$,

$${\bf r}={\bf \tilde{d} - d}. \nonumber$$

My research is focused on the attenuation/separation of the coherent noise only. The first strategy relates to fundamentals in inverse theory as detailed in the General Discrete Inverse Problem Tarantola (1987) and approximates the inverse covariance matrices with PEFs. The second strategy proposes to introduce a coherent noise modeling part in Equation 2. The noise operator will be a PEF. In the first strategy the coherent noise is filtered. In the second strategy the coherent noise is subtracted from the signal. The two methods should (1) give IID residual components, (2) stabilize the inversion, and (3) preserve the ``real'' events amplitudes as long as the noise and the signal operators have been carefully chosen.