Representing finite faults not collocated at a block boundary

[brendanjmeade]

Overview

• Currently, all faults are block-bounded. This is kinematically motivated.

• There may be other faults disconnected from major block boundaries that are no driven by block motion but by locally applied deformation at the BEL/CMI.

  • Traditionally, it's been difficult to reconcile the non-block boundary faults with far-field tectonic motions because there is no obvious "deep-dislocation" analog outside of two-dimensional cases.
  • However, if we only need local earthquake cycle effects and never need to generate far-field deformation from these truncated faults, then it's possible to represent their motion in a heuristic way. The core idea is to have a regular meshed fault that may or may not exhibit creep in places, and below that fault, introduce a BEL/CMI-like structure that generates local interseismic-like velocities (see cartoon below).
    • NOTE: Estimated slip on the known fault would not be slip-deficit in the block model sense. Instead, the fully locked case would be $s=0$, and any non-zero slip would be creep.
    • A localized BEL/CMI structure can readily produce something that looks like a local interseismic gradient but does not have to satisfy far-field block motion. In fact, this may be a means of imaging the distribution of locally applied BEL/CMI boundary conditions (e.g., in the Barbot sense).

Implementation/constraints

• I propose that this requires only two ingredients:
  1. A meshed representation of the "known finite fault" (pink fault below).
  2. A meshed representation of the BEL/CMI fault beneath it (grey fault below).
  • This only requires modification of input files.
• Constraints. Slip rate constraints are the most obvious starting point. However, one could imagine a case where a constraint links the two meshes above together. Something like the elastic slip rate on the upper mesh cannot be greater than the slip rate on the BEL/CMI mesh. This would effectively be a new type of "coupling-like" constraint that never involves kinematic slip rates but only elastic slip rates.
  • This requires modifying the estimation routine.

Illustration of basics

[brendanjmeade]

Take a look when you are bored @jploveless!

[jploveless]

This is really nice sketched out, and it has me thinking about various ways in which the kinematics could be considered within and/or tangential to a celeri run.

Am I understanding correctly that the slip rate distributions on the non-block bounding fault (NBBF) and the BEL would be estimated as part of a celeri run? The KL/QP estimator should work nearly as is, but the constraints would be different because the definition of coupling on the NBBFs is different.

The "ideal" estimation for a fully coupled strike-slip NBBF would be zero slip everywhere, with an interseismic gradient pattern estimated on the underlying BEL (i.e., top-to-the-north on elements lying to the west of a north-striking, right-lateral NBBF; top-to-the-south (or slower top-to-the-north) on the east side BEL elements), mimicking a deep dislocation pattern, though different because the NBBF is finite length. This may allow for a post-processing step that tries to translate the actual NBBF slip distribution into a quasi-coupling distribution. (I say quasi because we wouldn't have true kinematic slip rates.)

For the slip rate constraints that you mention, how you do envision applying those? As you said, non-zero slip rates estimated on the NBBF are actually creep rates. Could geologic slip rates on NBBFs somehow be mapped into an a priori slip rate distribution on the underlying BEL?

[brendanjmeade]

Am I understanding correctly that the slip rate distributions on the non-block bounding fault (NBBF) and the BEL would be estimated as part of a celeri run? The KL/QP estimator should work nearly as is

Yep!

With this approach, we can have both classes of faults in a single cogent model.

but the constraints would be different because the definition of coupling on the NBBFs is different.

Slip rate only constraints will work today because these are just other meshes. This new type of coupling will require a bit more work.

The "ideal" estimation for a fully coupled strike-slip NBBF would be zero slip everywhere, with an interseismic gradient pattern estimated on the underlying BEL (i.e., top-to-the-north on elements lying to the west of a north-striking, right-lateral NBBF; top-to-the-south (or slower top-to-the-north) on the east side BEL elements), mimicking a deep dislocation pattern, though different because the NBBF is finite length.

Exactly!

This may allow for a post-processing step that tries to translate the actual NBBF slip distribution into a quasi-coupling distribution. (I say quasi because we wouldn't have true kinematic slip rates.)

Agreed.

For the slip rate constraints that you mention, how you do envision applying those? As you said, non-zero slip rates estimated on the NBBF are actually creep rates.

In the desciption above I intended slip rate constraints to be implemented exactly as we already do them: setting minum and and maximum values for the mesh in the QP solve.

Could geologic slip rates on NBBFs somehow be mapped into an a priori slip rate distribution on the underlying BEL?

That's a wild and cool idea! If we add a geologic slip rate constraint as a QP constraint (this already works well), then we could create a new coupling style constraint (again, this will require some work, but I'm optimistic that it's doable).