Randomization of the index of refraction in the tropospheric propagation

New formulations of the Maxwell equations in a heterogeneous medium are given. The author shows that the depolarization of an electromagnetic wave depends on the orthogonal projection of the gradients of the ε and μ constants on the E&oarr;∧H&oarr; vector. The author shows that the colinearity of gradeε&oarr; and gradμ&oarr; requires that the electromagnetic wave is a locally plane wave. therefore with this condition fulfilled one is able to predict the propagation of an EM wave through the troposphere with knowledge of the gradient of the index of refraction. The author constructs a stochastic differential equation related to it and its reactualization uses the sampled data of this index in the troposphere. So one is able to predict the mean value and the covariance function of the amplitude phase and polarization of the received wave. The same method is applied to acoustical propagation