Pilot point parameter types (additive vs multipliers)

[robinkeegan]

This is a fairly general question. When using pilot points, I typically start with an array of constant values and apply a few multiplier pilot-point parameters that represent different spatial structures (e.g., local variability and broader-scale trends), followed by a global multiplier. Is there any literature/tutorial/workshop that discusses the advantages and disadvantages of using multiplier parameters versus additive parameters? I have the impression that IES tends to behave better with multipliers, though I’m not sure where I heard that or whether it’s true.

[rhugman]

Hi @robinkeegan -

tldr: I dont know of any published paper/tutorials on this. Below is my poorly written understanding.

ies tends to behave better with the global & ppoint/grid scale multipliers, because the global multiplier provides strong sensitivity to "all" obs, allowing ies to correct for large-scale bias first. When combined, you get a hierarchical sensitivity: early iterations tend to update the global multiplier (big, robust change), later iterations tweak the local multipliers.

I would assume (no data!) that the same would apply for combination of global & ppoint/grid for additive parameters. Essentially because the global scale par provides the big knob and the others provide the smaller fine-tuning knobs.

that being said, most subsurface props vary over a big range and are kinda log-normal, so changes are more like scaling than adding. using multipliers lets ies make proportional tweaks. Also, uncertainty tends to be proportional to magnitude. By using a multiplier, unc is implicilty sclaed to the prior mean magnitude.

[robinkeegan]

Thanks Rui, That makes a lot of sense to me. Anecdotally, I have observed similar behavior with my models where the large scale parameter is adjusted first and the local multipliers are adjusted later. It would be interesting to do a comparison of the different approaches (additive vs multiplier), direct vs global + local, etc. Could be an interesting case study for the next AGC...