STRATIGRAPHIC FILTERING .1. DERIVATION OF THE ODOHERTY-ANSTEY FORMULA

The authors present a new and more detailed derivation of the formula due to O'Doherty and Anstey (1971) for filtering a transmitted wavelet by short-period multiples. They use a continuous rather than discrete formulation and regard the impedance as a random variable. The mean pressure represents the downgoing wavelet as progressively modified by short-period multiples, while the deviations from the mean field are essentially the upcoming reflections. Standard procedures and approximations lead to the dispersion relation of the mean pressure field. To describe the stratigraphic filtering, they introduce a dimensionless complex quantity F such that a wavelet which has traveled a time DELTA T is modified by the filter.