What do seismic waves look like when they propagate through multiple layers of different velocity?
In this document we will explore the different types of seismic ray paths in a three layered earth, seeing how they depend on layer depth and velocities.
To learn more check out the online resource for Geophysics for Practicing Geoscientists, much of the text content here was adapted from that resource.
Consider a P-wave which is incident at an angle $\theta_1$ measured with respect to the normal of the interface, as seen in the figure below where the approaching wave is represented as a ray.
The angles of the reflected and refracted rays are as follows:
Snell's Law for two layers where $v_1$=
When the wave in the second medium is critically refracted, it travels parallel to the interface at a speed of $v_2$. As it travels, it radiates energy into the upper medium with the associated ray path making an angle $\theta_c$ with the normal. This critically refracted wave is also called a "head wave". It is somewhat analogous to the bow wave of a moving boat.
Try adjusting the velocity of each layer using the controls on the right and adjust the depth of each layer by dragging the vertical sliders on the ray path plot. You can adjust the receiver offset by dragging the node on either plot. Finally, you can use the horizontal slider on the travel-time plot to explore how the rays progress as time advances. On the top plot, the path of each ray up to the time specified by the time slider are shown as thick solid lines. Thin dashed lines show how the rays will continue to propagate after the specified time. The travel-time vs offset plots for the refracted rays will be dashed for offsets at which the rays will arrive after the direct wave.