Error measures for tomographic estimates of sound velocity

Inversion of perfect (error-free) tomographic data produces an imperfect estimate of the sound speed anomaly. The estimate is in error because the unknown function is sampled by a finite number of rays. This imperfection of the measuring system can be interpreted either in terms of resolution or in terms of bias error. In certain instances, the bias interpretation offers significant advantages, particularly when one wishes to quantify the error in the estimate. In this paper, we develop the latter interpretation. Our treatment employs various moments of the resolution kernels of the Backus-Gilbert theory. Methods for calculating bias error bounds as combinations of constants, dependent only on the tomographic configurations, and bounds on the higher order derivatives of the estimated function will be shown. Calculated bounds for a sample configuration will be presented. Use of these bias constants in comparisons of configuration performance will also be discussed.