Data dependent parameterization and covariance calculation for inversion of focusing operators

Barbara E. Cox

B.E.Cox@ctg.tudelft.nl

ABSTRACT

The Common Focus Point (CFP) method makes it possible to convert conventional two way traveltimes to focusing operators that represent one way traveltimes. These focusing operators are inverted to obtain a velocity model. The under-determined nature of the inversion problem is addressed by the data dependent adjustment of the parameterization by means of the a posteriori covariance. This results in an efficient, non-laborious algorithm producing well determined inversion problems. The required a posteriori covariance is normally explicitly solved in the explicit matrix calculation during optimization. However, these explicit calculations are not feasible in larger problems. Fortunately, algorithms have been proposed to extract the a posteriori covariance from the more efficient approximate matrix inversion algorithms that are available.