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A key element in drill steering and prediction of lithology ahead-of-the-bit is the transmission of while-drilling information from the bottom of the well to the rig operator and the geophysicists. Mud-pulse telemetry, based on pressure pulses along the drilling mud and extensional waves through the drill string, is the most used technique. The last method, properly designed, could transmit data rates up to 100 bits per second, against the 1 or 2 bits per second achieved with pressure pulses. In this work, a time-domain algorithm is developed for the propagation of one-dimensional axial, torsional, and flexural stress waves, including transducer sources and sensors. In addition, the equations include relaxation mechanisms simulating the viscoelastic behavior of the steel, dielectric losses, and any other losses, such as those produced by the presence of the drilling mud, the casing, and the formation. Moreover, the algorithm simulates the passbands and stopbands due to the presence of the coupling joints and pulse distortion and delay due to nonuniform cross-section areas. Acoustic and electric pulses, generated at one location in the string, can be propagated and detected at any other location by piezoelectric and acoustic sensors, such as PCB accelerometers, clamp-on ammeters, force, and strain transducers.

Abstract:The virtual reflector method simulates new seismic signals by processing traces recorded by a plurality of sources and receivers. The approach is based on the crossconvolution of the recorded signals and makes it possible to obtain the Green's function of virtual reflected signals as if in the position of the receivers (or sources) there were a reflector, even if said reflector is not present. This letter presents the virtual reflector theory based on the Kirchhoff integral representation theorem for wave propagation in an acoustic medium with and without boundary and a generalization to variable reflection coefficients for scattered wavefields.

We discuss the use of autocorrelogram interferometry by using noise from the tunnel-boring machine (TBM). The TBM provides seismic signals/waves while drilling in a tunnel (TSWD). The tunnel geometry, unlike a reverse vertical seismic profile (RVSP) using a drill bit, makes it possible to record the waves reflected from the region between the tunnel face and the projected tunnel exit and those transmitted ahead of the tunnel face. We processed the waves recorded at back positions with respect to the TBM in a manner similar to a RVSP data set obtained by conventional reference-correlation techniques. We processed the waves transmitted ahead of the TBM using autocorrelogram interferometry techniques. Using these wavefields offers advantages over conventional borehole drill-bit vertical seismic profiles (VSPs). The most important advantage is getting reflections from the transmitted (front) wavefield by utilizing Kunetz’s equation and reversed-time traces. The approach also improves the analysis of the transmitted amplitudes. Finally, we improved the deconvolution of the reflected (back) waves by using the transmitted wavefields measured for interferometry purposes. In particular, by using both front (transmitted) and back (reflected) waves, it is possible to deconvolve the signature of the source extended spatially along the tunnel axis. We use a 1D model in which the interfaces are assumed subvertical. We present a case history in which TSWD data were acquired in a tunnel measuring [Formula: see text] long. We compare results from the transmitted reversed-time and back-reflected waves ([Formula: see text]-waves) with those obtained by amplitude analysis and estimation of reflection coefficients. Each approach matches the interpretation of the fractures encountered in the tunnel.