** Next:** Interpolation of bathymetry data
** Up:** Multidimensional seismic noise attenuation
** Previous:** Adaptive subtraction of multiples

Chapter tackles the noise problem generated
by modeling uncertainties. Using the mathematical framework of
least-squares inversion, it is theoretically possible to eliminate the
noise present in the data by estimating the data covariance operator
Tarantola (1987). The data covariance operator can be seen as a
filtering operator that operates in the data space. Building on
Nemeth (1996), it is also possible to separate noise and signal
by incorporating a noise modeling operator within the inversion.
In both techniques, the residual components become independent and
identically distributed (IID). In Chapter , I
review both approaches and show that multidimensional prediction-error
filters (PEFs) can approximate covariance and modeling operators.
In addition, I unravel the mathematical links between the
two approaches and establish that the noise modeling technique
can be algebraically reduced to a filtering method with projection operators.

** Next:** Interpolation of bathymetry data
** Up:** Multidimensional seismic noise attenuation
** Previous:** Adaptive subtraction of multiples
Stanford Exploration Project

5/5/2005