Abstract
Todoeschuck and Jensen recently reported that the reflectivity sequences, denoted μ(k) calculated from some sonic logs are not white and have a power spectra! density approximately proportional to frequency, called a Joseph spectrum. In this correspondence, we show how to compute the minimum-variance estimate μMV(k) and maximum-likelihood estimate μML(k) for a μ(k) modeled as a nonwhite Bernoulli-Gaussian (B-G) process with a Joseph spectrum. We also present the corresponding μMV *(k) and μML *(k) for a statistically equivalent white B-G process μ*(k) which mimics μ(k). Through some simulations, we conclude that μMV *(k) = μMV *(k) and μML *(k) = μML *(k) for a white B-G process μ(k) and that μMV *(k) and μML *(k) are acceptable for the estimation of μ(k) when μ(k) is nonwhite with a Joseph spectrum. © 1992 IEEE