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The effect of gradually increasing velocity with depth in compacted sedimentary layers is described by asymptotically bounded velocity models. These models are defined by three intuitive parameters: the velocity, its vertical gradient at an initial depth level, and a bounded velocity value. Recently, we have introduced the exponential asymptotically bounded (EAB) model, which belongs to this family of velocity models. We introduce another monotonically increasing and asymptotically bounded model, which approaches the asymptotic value in a slower and smoother fashion. Its main attractiveness is the simplicity of ray tracing. The ray trajectories in this model are elliptic, hyperbolic, or parabolic curves, depending on the ray parameter (horizontal slowness). The linear velocity model with a circular trajectory is a particular case of the proposed model. Because the shapes of the ray trajectories correspond to the three types of conic sections, we call the model Conic. We derive the relationships for lateral propagation distance, traveltime, and arc length of the raypath for arbitrary nonvertical rays, and we develop procedures for initial value and boundary-value ray tracing. Both ray-tracing problems have an analytical closed-form solution.
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