Interpolation of 2-D vector data using constraints from elasticity

Paul Wessel, & David T. Sandwell

Published October 28, 2016, SCEC Contribution #7982

We present a method for interpolation of sparse two-dimensional vector data. The method is based on the Green’s functions of an elastic body subjected to in-plane forces. This approach ensures elastic coupling between the two components of the interpolation. Users may adjust the coupling by varying Poisson’s ratio. Smoothing can be achieved by ignoring the smallest eigenvalues in the matrix solution for the strengths of the unknown body forces. We demonstrate the method using irregularly distributed GPS velocities from southern California. Our technique has been implemented in both the Generic Mapping Tools and MATLAB®.

Citation
Wessel, P., & Sandwell, D. T. (2016). Interpolation of 2-D vector data using constraints from elasticity. Geophysical Research Letters, 43(20), 10,703-10,709. doi: 10.1002/2016GL070340.