Full Waveform Inversion of P Waves for V[subscript s] and Q[subscript p]

Abstract

We present an indirect method of determining shear wave velocities from full waveform acoustic logs based on the inversion of the spectral ratio of the P-wave trains at two source-receiver separations. This method simultaneously inverts for the formation shear wave velocity and compressional wave attenuation. The P-wave response is calculated by means of branch-cut integration. This method is useful in "soft" formations where the shear wave velocity is lower than the acoustic velocity of the borehole fluid and thus there are no refracted shear wave or pseudo-Rayleigh wave arrivals. The method is shown to give good estimates of formation shear wave velocity in both synthetic and field data. The inversion algorithm is sensitive to local minima; care must be taken to avoid them.