Attenuation is the anelastic process which dissipates seismic energy by conversion to heat, thus decreasing the amplitude and modifying the frequency and phase content of a propagating wavelet. Laboratory measurements show seismic phase velocity and attenuation are dependent upon the fluid saturation and the product of frequency and pore-fluid viscosity, with a peak in attenuation between the seismic and sonic bands.The dominant mechanism by which seismic energy is dissipated in the upper crust is local viscous fluid flow in pores of small aspect ratio. Phenomenologically, this behavior is modeled as a series of linear viscoelastic elements with a narrow distribution of relaxation times, where velocity and attenuation are related through the Hilbert transform. This model may be generalized to include constant-Q behavior, as observed in dry rocks. Solutions to the wave equation may be generated for an arbitrary frequency dependence of phase velocity and Q. When Q is nearly independent of frequency, the impulse response is asymmetric and the power spectrum is a straight line with slope proportional to Q. When Q is roughly proportional or inversely proportional to frequency, the impulse response is nearly symmetrical and the power spectrum is nonlinear.These results indicate that the frequency content, phase spectrum, and velocity may be strong indicators of the type of pore fluid in a formation. Alternatively, if the type of pore fluid is known, these attributes could be used to monitor temperature changes of a formation.

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