VELMAP-style strain rate method?

[jlmaurer]

VELMAP is a (non-open-source) code for computing strain rates from GNSS and InSAR. Original reference is Wang & Wright, 2012, but used more recently by Weiss et al. (2020). The methodology is pretty simple, basically the following:

• Divide the region into cells (Wang & Wright use triangular cells) and assume the velocity only varies linearly with position inside each cell.
• Define interpolation kernels for GPS, InSAR, whatever other datasets you have.
• If both InSAR and GPS, define the kernel for removing a bi-linear plane from the InSAR to match the GPS
• impose Laplacian smoothing on the interpolated field
• Solve for the velocities in the cells using least-squares that best match the observations

Should we implement this method and add it, or simply add it to the list of non-implemented methods?

[jlmaurer]

@kmaterna Re our conversation earlier I'm going to check whether VISR or Huang's method may be similar to this one.

[jlmaurer]

Just for documentation on Huang's method and how it compares to VELMAP.

Huang method:

• Solves for gradients within a grid area by averaging the gradients between the grid center and all data points
• Can weight data by distance or otherwise
• Could solve directly for gradients and displacements
• Smooths by averaging over a neighborhood of a fixed size

VELMAP:

• Based on papers by England and Molnar (1997; 2005)
• Solves for velocities in (generally triangular) elements, assuming that strains are constant (i.e. velocities are linear) within the elements
• The original paper was to solve for velocities given strain rates calculated from faults; the later applications from Wang & Wright (2012) and Weiss et al. (2020) use the same interpolation kernels but solve for strain rate from velocities.
• Smooths by imposing that the velocity field is second-order smooth (i.e. minimizes second-order derivatives)