An analytic generalized inverse for common-depth-point and vertical seismic profile traveltime equations.

Presents an analytic formula for the generalized inverse matrix associated with vertical seismic profile (VSP) and common-depth-point (CDP) travel-time equations. Its functional form explicitly depends upon the source-receiver geometry and its validity is restricted to horizontally layered earth models where there is negligible ray bending. The importance of the generalized inverse is that it can be used to derive closed-form expressions for the covariance matrix, condition number, resolution matrix, and average inverse eigenvalues for the traveltime equations; these formulas are useful in designing source-receiver geometries which optimize velocity reconstruction by traveltime inversion. -from Author