Synthetic logs of multipole sources in boreholes based on the Kelvin–Voigt stress–strain relation |
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| Authors: | José M Carcione Flavio Poletto |
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| Institution: | Istituto Nazionale di Oceanografia e di Geofisica Sperimentale (OGS), Borgo Grotta Gigante 42c, 34010;Sgonico, Trieste, Italy. E-mail: |
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| Abstract: | We design a numerical algorithm for wave simulation in a borehole due to multipole sources. The stress–strain relation of the formation is based on the Kelvin–Voigt mechanical model to describe the attenuation. The modelling, which requires two anelastic parameters and twice the spatial derivatives of the lossless case, simulates 3-D waves in an axisymmetric medium by using the Fourier and Chebyshev methods to compute the spatial derivatives along the vertical and horizontal directions, respectively. Instabilities of the Chebyshev differential operator due to the implementation of the fluid–solid boundary conditions are solved with a characteristic approach, where the characteristic variables are evaluated at the source central frequency. The algorithm uses two meshes to model the fluid and the solid. The presence of the logging tool is modelled by imposing rigid boundary conditions at the inner surface of the fluid mesh. Examples illustrating the propagation of waves are presented, namely, by using monopoles, dipoles and a quadrupoles as sources in hard and soft formations. Moreover, the presence of casing and layers is considered. The modelling correctly simulates the features—traveltime and attenuation—of the wave modes observed in sonic logs, namely, the P and S body waves, the Stoneley wave, and the dispersive S waves in the case of multipole sources. |
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| Keywords: | Numerical solutions Fourier analysis Downhole methods Geomechanics Seismic attenuation Wave propagation |
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