Beam-intensity calculations with uncertain sound speed profiles

A nonsecular procedure is derived for modifying the intensity distribution I(μ) computed in a channel with a sound speed profile μ, so as to account for small changes Δμ in the profile. This procedure is then employed to relate the statistics of a random ensemble of profiles to the statistics of the corresponding intensity distributions. The difference between I (_〈μ〉)> the intensity distribution for the mean (expected) profile, and 〈I (μ)〉, the expected intensity distribution for the ensemble, is studied: it is taken as a measure of the relevance of/((//)) as an approximation. At very short ranges, the two quantities are identical. At very long ranges, I 〈I (μ)〉obliterates entirely the range dependence of I (_〈μ〉). The usefulness of I (_〈μ〉) as an approximation is therefore restricted to ranges up to some transition range r_T. The transition range is inversely proportional to the relative magnitude M of the deviation from the mean profile 〈μ〉, and also to ratios constructed from the characteristic (focusing) length of the channel, the injection depth of the beam relative to the channel axis, and the correlation length of the ensemble of profiles. Expressions for r_T are derived in several limiting situations, and potential applications are discussed.