I have tried using noise/blue etc. to create a similar effect. It looks similar but not quite as graduated. I'm interested in hearing about different approaches!
Color Burnto the noise layer
It's also implementable within just single Inner Glow style for a shape layer (the shape itself is painted black).
Let's go from top to bottom:
Try playing with the numerical values.
Start with solid shape centered on your canvas. Create a layer above the shape layer and add a radial gradient from the center of that shape to its edge. Create a reveal all mask on the shape layer and then copy and paste the gradient to the mask. Add noise to the original gradient layer and then use the subtract bending option.
That should get you close.