Wave-based imaging techniques are commonly used in geophysical and medical industries to obtain information about an unknown medium by measuring the travel time of reflected waves. For instance, in seismic exploration, seismic energy is used to probe beneath the surface of the Earth and is integral for exploration of economic deposits of oil, gas, or minerals, but also for engineering, archeological, and scientific studies. This is done either passively (using a naturally occurring earthquake) or actively (using a source of seismic energy, such as an explosive charge or seismic vibration) where energy is directed into the Earth. The echoes of seismic waves as they are reflected off of discontinuities in the subsurface are then measured across a measurement area. Similarly, medical ultrasonography is an imaging technique used to create an image of internal body structures such as tendons, muscles, joints, blood vessels, and internal organs. Ultrasound images, also known as sonograms, are created by sending pulses of ultrasonic waves into tissue using a probe. The ultrasound pulses echo off of tissues with different reflection properties and are returned to the probe, which records and displays them as an image. The mathematical foundation behind both of these applications is based on the classical Fermat's principle in physics: a wave takes a path between two locations that can be traveled in the least time. Travel time of a wave defines a mathematical model in which the d