Parameter Estimation Theory Bounds and the Accuracy of Full Field Inversions

Abstract

The Cramer-Rao parameter estimation bounds are derived to evaluate limits on the attainable accuracy for full field inversions. These bounds are applied to several inversion scenarios: i) matched field tomography for both narrowband and broadband signals, ii) broadband, full field tomography for coherent signals and iii) noise tomography. In the case of adiabatic propagation with a mode resolving receiver array these bounds specify the performance limits for full field inversions by both matched field and ocean acoustic tomography and they can be expressed in terms of the phase and group slownesses of the propagation and the mode functions at the source.