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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
| |
(2) |

where is a mapping of the data (unknown of the inverse problem), an operator
and the seismic data. The residual **r** is defined as the difference between input
data **d** and estimated data ,
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.

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Stanford Exploration Project

9/5/2000