Construction of Covariance Functions with Variable Length Fields

摘要

This article focuses on constructive development and application of covariance functions with length scales determined by certain prescribed functions. These reduce to covariance functions depending only on a length scale that have been widely applied in diverse applications where covariance models are required. Covariance modeling applications in the earth sciences are emphasized, where correlation length scales vary in altitude and/or on horizontal surfaces. In accordance with standard terminology, these covariance functions will be said to depend on a variable length field