Publications

Abstract not provided.

The parametric grid capability of the Knowledge Base provides an efficient, robust way to store and access interpolatable information which is needed to monitor the Comprehensive Nuclear Test Ban Treaty. To meet both the accuracy and performance requirements of operational monitoring systems, we use a new approach which combines the error estimation of kriging with the speed and robustness of Natural Neighbor Interpolation (NNI). The method involves three basic steps: data preparation (DP), data storage (DS), and data access (DA). The goal of data preparation is to process a set of raw data points to produce a sufficient basis for accurate NNI of value and error estimates in the Data Access step. This basis includes a set of nodes and their connectedness, collectively known as a tessellation, and the corresponding values and errors that map to each node, which we call surfaces. In many cases, the raw data point distribution is not sufficiently dense to guarantee accurate error estimates from the NNI, so the original data set must be densified using a newly developed interpolation technique known as Modified Bayesian Kriging. Once appropriate kriging parameters have been determined by variogram analysis, the optimum basis for NNI is determined in a process they call mesh refinement, which involves iterative kriging, new node insertion, and Delauny triangle smoothing. The process terminates when an NNI basis has been calculated which will fir the kriged values within a specified tolerance. In the data storage step, the tessellations and surfaces are stored in the Knowledge Base, currently in a binary flatfile format but perhaps in the future in a spatially-indexed database. Finally, in the data access step, a client application makes a request for an interpolated value, which triggers a data fetch from the Knowledge Base through the libKBI interface, a walking triangle search for the containing triangle, and finally the NNI interpolation.

The parametric grid capability of the Knowledge Base (KBase) provides an efficient robust way to store and access interpolatable information that is needed to monitor the Comprehensive Nuclear Test Ban Treaty. To meet both the accuracy and performance requirements of operational monitoring systems, we use an approach which combines the error estimation of kriging with the speed and robustness of Natural Neighbor Interpolation. The method involves three basic steps: data preparation, data storage, and data access. In past presentations we have discussed in detail the first step. In this paper we focus on the latter two, describing in detail the type of information which must be stored and the interface used to retrieve parametric grid data from the Knowledge Base. Once data have been properly prepared, the information (tessellation and associated value surfaces) needed to support the interface functionality, can be entered into the KBase. The primary types of parametric grid data that must be stored include (1) generic header information; (2) base model, station, and phase names and associated ID's used to construct surface identifiers; (3) surface accounting information; (4) tessellation accounting information; (5) mesh data for each tessellation; (6) correction data defined for each surface at each node of the surfaces owning tessellation (7) mesh refinement calculation set-up and flag information; and (8) kriging calculation set-up and flag information. The eight data components not only represent the results of the data preparation process but also include all required input information for several population tools that would enable the complete regeneration of the data results if that should be necessary.

The DOE Knowledge Base data storage and access model consists of three parts: raw data processing, intermediate surface generation, and final output surface interpolation. The paper concentrates on the second step, surface generation, specifically applied to travel-time correction data. The surface generation for the intermediate step is accomplished using a modified kriging solution that provides robust error estimates for each for each interpolated point and satisfies many important physical requirements including differing quality data points, user-definable range of influence for each point, blend to background values for both interpolated values and error estimates beyond the ranges, and the ability to account for the effects of geologic region boundaries. These requirements are outlined and discussed and are linked to requirements specified for the final output model in the DOE Knowledge Base. Future work will focus on testing the entire Knowledge Base model using the regional calibration data sets which are being gathered by researchers at Los Alamos and Lawrence Livermore National Laboratories.

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.