The overall spectra from the simulated volumes are as expected (Tribble 1993) with a little noise due to the finite size of the simulation. The spectrum from any small volume element has a sharp break, but the overall spectrum is a superposition of many spectra with different normalizations and break frequencies, leading to a smoothing out of the break (Tribble 1993). This is particularly noticeable for the high field, low diffusion simulation, as apparent in Fig. 7, while the other two models give spectra similar to the JP model, with a sharp break.

Fig. 7 The overall spectra for the three models considered in the text.

For individual points the averaging is over a smaller subset of the possible individual spectra so that the spectra from individual points show some variation. In the low field, high diffusion case, the pixel spectra are all very similar, varying primarily in normalization and break frequency but not in shape---they are simply shifted relative to each other. The intermediate case spectra are also similar. The spectra in the high field, low diffusion case show a much greater variation. This is consistent with the behaviour noted for the images, in which individual points in the high field strength simulation fade at very different rates.

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Peter Tribble, peter.tribble@gmail.com