How should I choose the block size in constrained model-based inversion?

Question

In constrained model based inversion, block size (in ms) is one of the inversion parameters. Specifying the block size value in the software divides the pseudo-velocity log into that number of layers or blocks. A smaller block size means higher resolution but that doesn't mean that one should specify smallest value because sometimes inversion result gets unstable. So how should one assign the block size parameter in model-based inversion?

Answer 1

It depends.†

Some factors to consider:

• The sample interval of your seismic data. there's not a lot of point in being smaller than that. For most legacy data it's 4 ms; these days it's often 2 ms. This is a lower bound; you can increase from here if your data have limited bandwidth; there's no point using less than 8 ms for data that's just noise past 50 Hz.
• What is the scale of your problem? If this is part of an exploration exercise and the model is areally large, then you can safely and justifiably lose temporal resolution. If it's a reservoir characterization problem, then there's probably some feature you really care about: minor reservoir units, thin heterogeneities, etc.
• How much time have you got? Small samples means more compute time, more statistics, more fiddling with details. It also means more time to simulate later, if you're doing flow modeling. Since you will no doubt end up doing everything multiple times, you need a model that is both useful and iterable.

I think there are at least a couple of approaches that avoid having to choose now and stick with it:

1. Start large, figure out the workflow, then reduce the size and watch the stability. Iterate until you have the right combination of detail, stability, and convenience.
2. Model the big picture at low resolution, and more interesting subsets of the data at high resolution. Make the large interval an integer multiple of the small to facilitate merging them later.

Note that some properties, such as velocity, are scale-dependent. Be careful how you upscale them. Read up on Backus averaging, starting with Chris Liner's recent work.

† How's that for a geoscientists's answer?