Stochastically excited waves in a 1D random medium – the mean field and power spectrum

Abstract

Sciilar wave propagation is examined when both the wave source iind the propagation speed are random. Resuits arc derived tor the nieiiii Held and the power spectrum using tiic scLond-order Bom approximatinn. The results depend on whether the source .S(.v. /) and the propagation speed t(.i, f) are correlated or mit. When they are uncorrelated. the mean held is zero. When they are correlated, the mean ticid is non-zero only when the source is non-station;iry. The power spccrrum is incohcreni to leading order. There is a Iranslcr of energy from lower to higher Ireqiiencies awing to wave scattering. The corresponding frequency upshift of the power prolile in the ik.o)) domain is mainly caused by the cross power between the direct and the twice scattered held, which represents a second-order incoherent power contribution. The results are confirmed using a numerical solution of ihe wave ei;iia!ion where Ihe scattered held is e.xpanded to lifth order.