Comments on modeling the sound fields in an irregular ocean by causal first-order equations

Two comments on using the causal matrix equations derived earlier for modeling the sound fields in a horizontally irregular medium are presented. The comments should be taken into account in practical calculations. The first of them is concerned with the discontinuities in the parameters of the medium along the propagation path. To eliminate the problems arising in this case, the mode evolution equations are modified to the case of matched boundaries of the irregular region and the layered part of the medium. The second comment refines the description of the specific case of a two-dimensionally inhomogeneous medium with the azimuthal symmetry in the horizontal plane. To reformulate the boundary-value problem to the problem for equations with initial conditions, the consideration of the more general three-dimensional initial problem with an azimuth angle is proposed with the sound source positioned at an arbitrary distance from the origin of coordinates.