ABSTRACT
Correlation is generally associated with statistics and the degree to which two random quantities are related. The concept may be extended to non-random signals that have definite structure, although in many cases there is a physical reason for the correlation that is better explained by an analytic model based on well founded theory. Correlation functions and their cousins, the covariance functions, play a significant role in the statistical analysis of random signals and associated optimal estimation theory and geostatistics. Correlation in statistics is defined usually as the normalized covariance between two random variables, that is, the covariance divided by the square root of the product of the variances of the two variables. Randomness is a state of uncertainty or non-determinism, and working with such a state requires a concept of probability. A cousin of the covariance function is the variogram, which plays a critical role in the optimal prediction and interpolation of random geophysical processes using the method of kriging.
