The image source method is an efficient way to perform a sound-speed tomography for seafloor characterization. To date, however, it has been limited by a locally range-independent approximation. In other words, the layer boundary had to be parallel and flat within the Fresnel zone of the measurement system. Here the method is extended to take into account realistic variations of interface dip angles. To do so, the elliptical wavefront shape approximation of the reflected waves is used. This permits a fairly simple equation relating travel time to the sine of the dip angle, and consequently to an equation for the equivalent medium sound speed. The Radon transform is exploited to extract the dip angle. Simulations with varying layer dip angles and curvature provide insight into the strengths and limitations of the method.