Performance bounds on geoacoustic inversions

Abstract

Lower bounds on the mean square error for parameter estimates using geoinversion methods are developed in terms of the tomographic version of the Cramer Rao bound. Two approaches are considered: (i) an active, coherent source with known waveform and time synchronization as in ocean acoustic tomography (OAT) and (ii) a passive, broadband source with known spectrum but with no time synchronization as in matched field tomography (MFT). Both approaches assume the receiver to be an array, e.g., vertical line array or towed horizontal line array (HLA). The formulation requires specifying the Green's functions connecting source and the sensors of the receiving array. The bounds demonstrate (i) OAT performance depends upon the mean square group speed spread of modes and (ii) MFT performance depends upon the phase speed spread where both are integrated across the band of the respective sources. The bound also indicates the coupling among parameter estimates. Uncorrelated estimates are usually desirable for efficient parameterization formulations. An example using a Pekeris waveguide with three unknown parameters: the ocean and bottom sound speeds and the depth. The extension to Bayesian problems where a joint a priori probability is given. This permits the evaluation enabled by the observed data.