Nonuniqueness of extreme acoustic-intensity tails in paraxial propagation through finite-order-matched intermittent media

Abstract

The determinacy of the extreme-intensity distribution after coherent diffraction by finitely many statistics of a random acoustic medium is examined. In a paraxial model driven by bounded marked Poisson events, the linear intensity response has an exact compound-Poisson law. For every prescribed finite even order, nonzero mark distributions are constructed whose complete medium cumulant functions agree through that order while their propagated distributions differ. This distinction is transferred to sufficiently weak finite-coupling propagation by a unitary-propagator bound. The effect is verified by deterministic inversion and independently sampled paraxial calculations for media matched through fourth order and for an equal-rate nonzero-mark control. For bounded response jumps, the far tail is shown to obey $-\log\Pr(Z>z)\sim z\log z/b$; the first correction depends on the endpoint geometry of the diffractive response. Two finite-threshold tail-ordering crossings are resolved, and coupling-dependent windows are identified by paired calculations in which the linear tail predicts full propagation to a declared tolerance. Hence a power spectrum, or any fixed finite collection of medium cumulants, is insufficient for exact prediction of acoustic extreme-event probabilities in this model.