Shot Records

Part 4, Part 4: The Acoustic Wave Equation

Learning objectives

  • Generate a shot record by propagating a source through a layered earth
  • Identify the direct arrival and the reflection hyperbolas
  • Explain moveout as traveltime increasing with offset
  • See what the wave equation makes that convolution cannot

What the Engine Is For

Part 4 built the acoustic wave equation, discretized it, tamed its stability and dispersion, and cleaned up its edges. This closer runs it for real and produces the thing that justifies all of it: a shot record. A source fires at the surface, the engine propagates the wavefield through a layered earth, and a line of receivers writes down what comes back.

Shot recordsthe wavefieldthe shot recordThe wave equation makes what convolution cannot: a direct arrival and curved reflection hyperbolas.

Reading the Record

Watch the record fill in and the physics is legible. The first, straight, steeply-dipping event is the direct arrival, energy that runs along the surface from source to receiver. Below it, each velocity layer returns a curved reflection hyperbola: the traveltime is shortest at the receiver right above the source and grows with distance, because energy going out to a far receiver travels farther. That growth of traveltime with offset is moveout, and it is the single most important thing a shot record carries that a zero-offset section does not.

Move the source and every hyperbola shifts its apex with it, because the geometry that made it has moved. This offset information, absent from the convolutional model by construction, is exactly what migration uses to put reflectors in their right place and what full-waveform inversion uses to recover velocity. The convolutional model of Parts 2 and 3 could never make a shot record; it only ever gave a post-stack, zero-offset trace. That is the boundary this whole part crossed. In Part 5 the same engine goes further still, turning the ghosts of Part 3, the diffractions, multiples, and bowties, into computed events.

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