In the ocean, coastal slope regions are of primary importance for both practical purposes and research, including acoustic studies. A typical coastal slope region has the form of a wedge with the angle between the sea surface and the bottom reaching ~0.005-0.01 rad; this region extends for several tens of kilome ters (or more) from the coast to the shelf edge, where the sea depth is about 200-350 m. Beyond this line, the sea depth begins to increase steeply (the continen tal slope). In the theoretical studies of sound propaga tion, the coastal slope is usually described by a wedge shaped model region with a constant velocity of sound and with ideally or nonideally reflecting boundaries [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. The solution to the problem on the field in an ideal wedge can be constructed by using, e.g., imagi nary sources, in analogy with the well known Pekeris model [6]; in this case, the imaginary sources are posi tioned in a circle [15,16]. In [1,9,15,16], the field in the wedge is constructed in a cylindrical coordinate system (the z axis coincides with the edge of the wedge) based on modes depending on angle ϑ in the vertical plane. A somewhat different approach is pos sible in the case of a smooth dependence of the sea depth on the distance to the coast (a small slope), when the wedge shaped region can be considered as a waveguide with varying depth and, in terms of the depth dependent field expansion in modes, the field can be described in the adiabatic approximation (ignoring the mode coupling). In the two dimensional version of the problem, where the field only varies in the vertical plane, one of the main features of sound propagation up the slope is the appearance of the crit ical cross section for a mode of a fixed number at a fixed frequency with decreasing depth and the reflec tion of this mode; or, the transformation of the mode in a leaky one and, hence, its escape to the bottom at a certain distance from the edge, this distance being dif ferent for different modes and frequencies [3, 7-9]. The three dimensional problem was considered in studies of the horizontal refraction of the acoustic field in a coastal slope region in both experimental (labora tory experiments [1, 11, 12] and full scale experiments in a coastal slope region [13]) and theoretical investi gations [1,[4][5][6]. In the latter, the field behavior was described in terms of vertical modes and horizontal rays [14] or numerically [17] by a parabolic equation (see references in [17]). For the ideal wedge model, the ray equations in the horizontal plane have analytic solutions [4][5][6] describing the position and shape of rays and caustics in the form of hyperbolas. In this case, in a wedge with ideally reflecting surfaces, two rays (the direct ray and the reflected, or, refracted, one) arrive at each of the points of the horizontal plane, and the corresponding interference pattern is formed. We note that, for a more realistic model (a nonideal bottom, a coordinate dependent sound velocity), the fiel...