Knowledge base interpolation of path-dependent data using irregularly spaced natural neighbors

This paper summarizes the requirements for the interpolation scheme needed for the CTBT Knowledge Base and discusses interpolation issues relative to the requirements. Based on these requirements, a methodology for providing an accurate and robust interpolation scheme for the CTBT Knowledge Base is proposed. The method utilizes a Delaunay triangle tessellation to mesh the Earth`s surface and employs the natural-neighbor interpolation technique to provide accurate evaluation of geophysical data that is important for CTBT verification. The natural-neighbor interpolation method is a local weighted average technique capable of modeling sparse irregular data sets as is commonly found in the geophysical sciences. This is particularly true of the data to be contained in the CTBT Knowledge Base. Furthermore, natural neighbor interpolation is first order continuous everywhere except at the data points. The non-linear form of the natural-neighbor interpolation method can provide continuous first and second order derivatives throughout the entire data domain. Since one of the primary support functions of the Knowledge Base is to provide event location capabilities, and the seismic event location algorithms typically require first and second order continuity, this is a prime requirement of any interpolation methodology chosen for use by the CTBT Knowledge Base