Solution of the fundamental problem of transient acoustic propagation in a borehole with the hybrid method

Abstract

The fundamental acoustic logging problem of a pulsed point source surrounded by both vertical and horizontal boundaries is solved with the hybrid method. The hybrid method yields the complete synthetic waveform including the head wave and the normal mode arrivals. The essence of the hybrid method consists in converting the head wave branch-cut contribution into discrete modes which, together with the normal modes, form a complete basis for the solution in each region. Boundary conditions at the horizontal bed boundary then couple the modes between different regions and enable the solution to be expressed in terms of reflection and transmission matrices of modes. Numerical results are illustrated as a function of the formation parameters. Transmission coefficients of head waves are calculated. The advantages of the hybrid method are also discussed.