**2.3. Ray optics and Green's Law approximations for tsunami waves**

Traveling waves, such as tsunami or electromagnetic waves, sometimes follow simple ray optics approximations where they can refract, changing their direction continuously with the refractive index. The refractive index for waves of any nature propagating through media with different or changing properties is defined as the ratio of the reference phase velocity to the phase velocity at the specific point in the medium. For light or electromagnetic waves, the reference velocity is taken as the speed of light in vacuum. For acoustic waves or water waves in the shallow‐depth limit, one normally selects a convenient reference velocity [10]. So, for example, if one selected the 4000‐m depth which is typical of a deep ocean basin, the refractive index becomes 4000/, which is sometimes referred to as the HF asymptotic limit. This approximation applies only when refractive index varies slowly and smoothly with distance. This means that the refractive index cannot have a discontinuous jump, for example, if the bottom had a significant change in depth over scales shorter than a wavelength, say 10 km. Bottom depth fluctuations over smaller scales are not important to tsunami propagation. The tsunami wave, with its massive inertia, is like a low‐pass spatial filter that effectively averages across these fine‐scale features. A wave typically does not respond appreciably to perturba‐ tions with a scale much smaller than its wavelength; this is sometimes known as the Rayleigh criterion. As tsunami wavelengths exceed tens of kilometers, this implies that perturbations with smaller spatial scales (e.g.10 km) are unimportant. There is an often‐asked question: "Do I need to use a bathymetry database for tsunami near‐field modeling with 1–2 km resolution?" The answer is "No: 10 km resolution is always adequate."

We now examine simplifications possible when depth varies slowly, and discuss exact alternatives that will work when depth varies abruptly.
