Simulation of borehole sonic waveforms in dipping, anisotropic, and invaded formations

Abstract

A numerical simulation study has been made of borehole sonic measurements that examined shoulder-bed, anisotropy, and mud-filtrate invasion effects on frequency-dispersion curves of flexural and Stoneley waves. Numerical simulations were considered for a range of models for fast and slow formations. Computations are performed with a Cartesian 3D finitedifference time-domain code. Simulations show that presence of transverse isotropy (TI) alters the dispersion of flexural and Stoneley waves. In slow formations, the flexural wave becomes less dispersive when the shear modulus (c 44) governing wave propagation parallel to the TI symmetry axis is lower than the shear modulus (c 66) governing wave propagation normal to the TI symmetry axis; conversely, the flexural wave becomes more dispersive when c 44 > c 66. Dispersion decreases by as much as 30% at higher frequencies for the considered case where c 44 < c 66. Dispersion of Stoneley waves, on the other hand, increases in TI formations when c 44 > c 66 and decreases when c 44 < c 66. Dispersion increases by more than a factor of 2.5 at higher frequencies for the considered case where c 44 < c 66. Simulations also indicate that the impact of invasion on flexural and Stoneley dispersions can be altered by the presence of TI. For the case of a slow formation and TI, where c 44 decreases from the isotropic value, separation between dispersion curves for cases with and without the presence of a fast invasion zone increases by as much as 33% for the flexural wave and by as much as a factor of 1.4 for the Stoneley wave. Lastly, presence of a shoulder bed intersecting the sonic tool at high dip angles can alter flexural dispersion significantly at low frequencies. For the considered case of a shoulder bed dipping at 80 , ambiguity in the flexural cutoff frequency might lead to shear-wave velocity errors of 8%-10%.

Acoustoelastic effects of Stoneley waves in a borehole surrounded by a transversely isotropic elastic solid

“…The low-frequency velocity (approaching the tube wave at 0 Hz) of Stoneley mode is controlled by c 66 , and c 44 governs the degree of dispersion with increasing frequency, when the borehole axis is along the formation axis of symmetry. 35 The results (solid line) of formation A show that the Stoneley phase velocities become big and the change of Stoneley dispersions is an approximate translation from the reference state v R ST . However, the results (solid line) of formation B show that the change of Stoneley dispersions is not an approximate translation from the reference state v R ST .…”

Repulsion of dispersion curves of quasidipole modes of anisotropic waveguides studied by finite element method

“…Usually, they are treated either by the perturbation theory or by the direct three-dimensional (3D) modeling. [1][2][3] Recently, it was proposed to address such problems by the pseudospectral method and by the generalization of the Riccati equation for the matrix impedance operator. 4,5 Alternatively, variational methods have been developed.…”