A passive acoustic method for detecting environmentally dangerous gas leaks from pipelines and methane naturally leaking from the seabed has been investigated. Gas escape involves the formation and release of bubbles of different sizes. Each bubble emits a sound at a specific frequency. Determination of the bubble radius from the frequency of its signature passive acoustic emission by use of so-called Minnaert formula has a restricted area of applicability near the seabed. The point is that the inertial mass and the damping constant of the birthing bubble are markedly different from those of a free bubble. The theoretical model for the bubble volume oscillations near the seabed has been proposed and an analytical solution has been derived. It was shown that the bispherical coordinates provide separation of variables and are more suitable for analysis of the volume oscillations of these constrained bubbles. Explicit formulas have been derived, which describe the dependence of the bubble emission near a rigid wall on its size and the separation distance between the bubble and the boundary.