Ocean acoustic tomography: Rays and modes

Abstract

We have measured perturbation of the sound speed δC(x,y,z) (temperature) field within an ocean volume by repeated acoustic transmissions through the volume along many different ray paths i (Ocean Tomography Group, 1982). The data set consisted of ray travel time perturbations δti, and the sound field was obtained by inverse theory from a linear weighted sum δC(x,y,z)=ΣiAi−1 (x,y,z) δti, where Ai is the time spent by ray i in a differential volume centered on x,y,z. Here the method is extended to cases (e.g. the ‘axial’ ocean near a sound speed minimum) where ray theory is not applicable or not convenient. This is done by including in the data set the frequency perturbation δf of lower modes. The matrix A is generalized to a combination of ray weighting and mode weighting. The procedures are illustrated for bilinear and quadratic sound channels, corresponding to a last and first arrival, respectively, of the axial ray, and for a cosh z profile (surprisingly close to some measured equatorial sound speed profiles) where all rays arrive together. We use a northwest Atlantic profile for illustration of an actual case, and here we find overlapping arrival sequences which lead to additional complexities. All this is conveniently displayed in frequency‐time (ambiguity) diagrams. We discuss two inversion schemes: one based on Abel transforms and the other on numerical matrix inversions. The latter scheme is more straightforward for perturbations from a known initial state. The paper is a review of the underlying principles; application to measurements is planned in the near future.