Velocity Model Estimation by Inversion of Focusing Operators: About the <br/><br/>Resolution Dependent Parameterization and the Use of the LSQR Method

Friday, April 26, 2002 - 1:30pm - 2:30pm
Keller 3-180
Barbara Cox (Technische Universiteit te Delft)
One of the main goals of seismic processing is to obtain an accurate image of the subsurface. The quality of the result strongly depends on the accuracy of the velocity model of the subsurface. The Common Focus Point (CFP) method has proved to be an appropriate method for macro velocity model estimation: This method makes it possible to convert conventional two way traveltimes to focusing operators that represent one way traveltimes. These focusing operators can be inverted to obtain a velocity model. The inversion of one way traveltime data (focusing operators) obtained by the CFP method is inherently simpler than the inversion of conventional two way traveltime data.

A linearized optimization method is used to translate the traveltimes to model updates. The fact that the inverse problem is mixed-determined is addressed by the resolution dependent parameterization. This results in an efficient, non-laborious algorithm producing well-determined inverse problems. The required resolution is normally solved in the explicit matrix calculation during optimization. However, these explicit calculations are not feasible in larger problems. Therefore, the complete inverse problem is based on an efficient approximate matrix inversion method: LSQR. This method bears some very useful properties, that can be exploited to analyze the inverse problem.