Maximum likelihood dereverberation with applications in sonic well logging

In the sonic well logging application, an acoustic source and an array of receivers are deployed along the axis of a fluid-filled borehole for the purpose of learning about the formation [1]. Conventional sonic methods position the receiver array many wavelengths from the source and, in effect, perform a refraction experiment in the hole. In this paper, we introduce a new method in which a short-spaced array is used to perform a reflection experiment. Our interest is in the maximum likelihood estimate of the cylindrical wave reflection coefficient of the formation from measurements of the field within the borehole. The problem is fundamentally one of dereverberation and is nonlinear. We present an iterative ML solution which requires only linear estimation at each step. This solution is new and is based, on the iterative ML theory developed by Musicus [2]. Preliminary results are encouraging.