Minimum-variance deconvolution and maximum-likelihood deconvolution for nonwhite Bernoulli-Gaussian processes with a Joseph spectrum

Todoeschuck and Jensen (1988) recently reported that the reflectivity sequences, denoted p(k), calculated from some sonic logs are not white and have a power spectral density approximately proportional to frequency, called a Joseph spectrum. It is shown here how to compute the minimum-variance estimate and maximum-likelihood estimate for a μ(k) modeled as a nonwhite Bernoulli-Gaussian (B-G) process with a Joseph spectrum. Also presented are the corresponding estimates for a statistically equivalent white B-G process μ*(k) which mimics μ(k). Some conclusions regarding the acceptability of these estimates are drawn