MWD Downhole Signal Transmission Boundary Condition Analysis and Wave Deconvolution

When a Measurement While Drilling (MWD) mud pulser opens and closes to create acoustic pressure transient signals which encode binary data representative of formation properties, an pressure wave will travel uphole, at the same time, a complementary wave will travel down hole, reflect at the drill bit, then propagate uphole to join with the up going wave, and the two up going waves interact either constructively or destructively, even both. Because an area discontinuity generally exists at the MWD drill collar and drill pipe junction, this system also reverberates within the MWD drill collar as a standing wave, with some leakage into the drill pipe. The wave that ultimately leaves the MWD drill collar to travel uphole to the surface is “scrambled” in the sense just described and recovering the history in which the pulser opens and closes, which ultimately contains the complete sequence of down hole binary information, is very difficult, particularly at high frequencies when acoustic wavelengths are short. Because it is the focus that models the MWD pressure wave transmission condition and extracts the useful signal from the puzzled surface signal, many researchers and companies devote themselves to solve these problems. The present paper analyzes the acoustic pressure wave transmits boundary condition detail, and teaches how to model the pressure wave that ultimately travels up the drill pipe. Also, it teaches how to recover the history of pulser open and close motion when the pressure in the drill pipe is known at the surface from surface signal processing.