# ESS 136A: Animations of wave propagation

### by Paul Tackley Oct 1999

Produced by solving the wave equation on a computer.

### 1) Diffraction effects

• Downgoing plane wave pulse interacts with various barriers
• Huygens principle: each point on the wavefront acts as a source of secondary wavelets
• focus on what happens to the incident wave (and the first reflection)- ignore multiple reflections, reflections from the side of the box, etc.

a) Reflector with a gap - Huygen's principle. Only part of the wavefront gets through the gap. The energy that gets through the gap spreads spherically in the lower part of the box.

b) Half-width reflector - Edge diffractions. On the left (reflected) side, the wavefront gets reflected (with negative amplitude). On the right side, the wavefront continues on its way. Energy is scattered from the edge of the reflector, causing both incident and reflected energy to spread spherically from this point.

c) Isolated object - Wavefront healing. The wavefront is diffracted around the object, and some distance later the wavefront has 'healed' back to almost its original form, making it difficult to detect the object.

### 2) Refraction+reflection

• Plane wave interacts with a layer interface (lower layer faster).

a) Less than critical angle. Most of the wavefront penetrates the interface and is 'bent' according to Snell's law. A fraction of the wavefront is reflected.

b) Critical angle. Wavefront in the lower layer is vertical (ideally- the simulation is not perfect). Reflection is strong.

c) Greater than critical angle. Wave is completely reflected from the interface. Mulpile reflections are built up as it travels down the box.

### 3) Explosive source: Direct, reflected + refracted arrivals

• Many things to notice!
• Identify direct wave, reflected wave (-ve amplitude=blue), and refracted 'headwave' (+ve amplitude=red).
• Click on image below to view animation

Direct wave:

• Is almost vertical by the time it reaches the end of the box

Reflected wave:

• 1st arrives at surface when direct wave is ~1/4 across the box
• gradually catches up to direct arrival.
• has much higher amplitude once critical angle is passed

Refracted wave:

• moves fast in lower layer
• radiates energy back into upper layer (slanting line)
• first arrives at surface when direct wave is ~2/5 across box
• overtakes direct arrival ~1/2 way across box