Calculation and Implementation of the Gradient of the DSO Objective Function for the General Acoustic Model
We present in this paper the computation of the DSO objective function in the general acoustic case. In this model, the density and the velocity are functions of the space variables. We use a perturbational approach, justified by the separation of scales between the long and short wavelength components of the model. An extension of the adjoint state technique yields an accurate expression of the gradient of the DSO objective function. Then we use a finite difference approximation of the wave equation, and give in the discrete the case the expression of the gradient. We show in that case how to apply the principle of images so that the discrete operators involved are self-adjoint and give exact discrete integration by parts.
Citable link to this pagehttp://hdl.handle.net/1911/101788
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