Seismic Ray

a line normal to the front of a seismic wave propagating from the focus of an earthquake. The direction of a ray changes with a change in the velocity of seismic waves along the path of propagation. In a homogeneous, isotropic elastic medium with a constant velocity of wave propagation, a ray is a straight line. In a first approximation for the earth, velocity is taken to be a function of depth; as velocity increases with depth, the paths of the rays become curved, turning convexly downward symmetrically relative to the apexes of the rays. The equation for a ray is

where T is the ray’s travel time, Q is the epicentral distance in radians, R is the radius of the earth, V_r is the velocity of seismic waves along the ray, e(r) is the angle of inclination of the ray to the horizon at a depth corresponding to the radius r, e₀ is the angle of emergence of the seismic ray on the earth’s surface, and V₀ is the velocity at the earth’s surface.

Each ray has a deepest point with radius r_p. At this point, e = 0, cos e(r) = 1, and p = r_p/ V_rp.