Absorbing Boundaries

Part 4, Part 4: The Acoustic Wave Equation

Learning objectives

  • Explain why a finite grid edge reflects waves as artefacts
  • See the difference a sponge (absorbing) boundary makes
  • Relate absorbing boundaries to clean shot records
  • Distinguish an absorbing edge from a reflecting free surface

The Edge That Should Not Be There

The wave equation runs on a finite grid, but the earth it models has no edges. That mismatch causes a specific, avoidable artefact. Left as they are, the outer cells of the grid behave like a rigid wall: a wave that reaches them reflects straight back into the model, an event that no real survey would ever record because there is no such wall in the ground.

Absorbing boundariesThe dashed sponge band absorbs outgoing waves so the grid edge does not reflect them back.

Soaking Up the Wave

Watch the point source radiate a circular wavefront. With the sponge off, the front reaches the edges and bounces, and within a few frames the model is a mess of criss-crossing artificial reflections. Turn the sponge on and a band around the edges, marked by the dashed rectangle, quietly absorbs the outgoing energy so almost nothing returns; the wavefront reaches the edge and is simply gone.

The engine uses a Cerjan sponge, a taper that multiplies the wavefield by a factor just under one across a band of cells so the wave decays smoothly to nothing before it can reflect. It is why every wave-equation synthetic in this course, and the shot records in the next section, come out clean at the sides. There is one deliberate exception: the top of a marine model is often kept reflecting on purpose, a pressure-release free surface, because that edge is real and its reflections are the surface multiples of Part 5. Choosing which edges absorb and which reflect is part of setting up an honest model.

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