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## The heat-flow equation

The diffraction or migration equation could be called the wavefront healing'' equation. It smooths back together any lateral breaks in the wavefront that may have been caused by initial conditions or by the lens term. The 15 migration equation has the same mathematical form as the heat-flow equation. But the heat-flow equation has all real numbers, and its physical behavior is more comprehensible. This makes it a worthwhile detour. A two-sentence derivation of it follows.  (1) The heat flow Hx in the x-direction equals the negative of the gradient of temperature T times the heat conductivity .(2) The decrease of temperature is proportional to the divergence of the heat flow divided by the heat storage capacity C of the material. Combining these, extending from one dimension to two, taking constant and ,gives the equation
 (1)

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Stanford Exploration Project
10/31/1997