


 Waveequation tomography by beam focusing  

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To reliably estimate velocity using wavefield operators,
I introduce a new objective function that rewards flatness of
the correlation between source wavefield and receiver wavefield.
The proposed objective function is maximized as
a function of the slowness model through the application of
residual moveout operators to the correlation.
The first term of the objective function
measures the power of the stack over local beams
as a function of the local beam curvature.
Maximization of this first term ensures
global convergence in presence of large velocity errors.
The second term maximizes the global power of the stack
as a function of time shifts applied to the local stack over the beams.
Maximization of this second term helps the estimation of localized
velocity errors.
I tested the application of the proposed objective function
by computing its gradients for two simple problems:
the estimation of a large and spatially uniform velocity error and
the estimation of a spatially localized velocity error.
The computed search directions confirm the potential of
the proposed method and illustrate the different roles
played by the the local and the global terms of the objective function.



 Waveequation tomography by beam focusing  

Next: Bibliography
Up: Biondi: Beam waveequation tomography
Previous: Localized velocity error
20100519