85 3. Acoustic logging 3.3 Acoustic waves In a vertical well, monopole tools can enable the recording of five propagation modes: • refracted compression wave; • refracted shear wave, only in fast formations (VS > VP fluid); • fluid wave; • two dispersive guided modes, which are pseudo-Rayleigh waves and Stoneley waves: – Pseudo-Rayleigh waves are reflected conical dispersive waves (Biot, 1952) with phase and group velocities which, at low frequencies (<5 kHz), approach the S velocities of the formation, while at high frequencies (>25 kHz) they asymptotically approach the propagation velocity of the compression wave in the fluid. These waves exist only in fast formations. – Stoneley waves are dispersive interface waves. In fast formations, they have phase and group velocities that approach the fluid velocity at high frequencies asymptotically, and from a lower value. In slow formations, they are more dispersive and sensitive to the S-wave parameters of the formation. At low frequencies, Stoneley waves are analogous to tube waves observed in downhole (Chapter 1) and VSP (Chapter 2). Full waveform acoustic measurements are represented as constant offset sections or common transmitter or receiver point gathers, similar to those used in seismic surveys. An constant offset section or acoustic coring is a set of acoustic recordings represented as a function of depth, obtained with a fixed transmitter-receiver distance. Presented below is a set of common transmitter point gathers and a set of constant offset sections showing the different wave types that can be observed on these recordings. The common transmitter point gathers are synthetic seismograms that have been made using the modeling programs of Jacques Quiblier (1997). These programs enable the modeling of acoustic data in slow and fast formations. The formation is infinite, elastic and isotropic. It is defined by the propagation velocities of P-waves (VP) and S-waves (VS), by the density ρ, and two quality factors (QP, QS) that are characteristic of the attenuation. The well of constant diameter (16.1 cm) is filled with water (Vf = 1,500 m/s, ρf = 1g/cm3) and is of infinite length. The tool of infinite length has the acoustic properties of the fluid. It consists of a transmitter (monopole or dipole) and nine receivers (measuring points). The distance between the transmitter and the first receiver is 1 m. The distance between 2 consecutive receivers is 12.5 cm. The time sampling interval is 10 μs, the listening time 4 ms. At each measurement point, the algorithm calculates the three components of the displacement (Ur, Uθ, Uz: radial, tangential and vertical displacements) and the pressure P. In our simulations, the characteristics of the formations are: – for the slow formation (VS < well fluid velocity): VP = 2,760 m/s
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