Wave dispersion and attenuation in viscoelastic isotropic media containing multiphase flow and its application

In this paper, we introduce the complex modulus to express the viscoelasticity of a medium. According to the correspondence principle, the Biot-Squirt (BISQ) equations in the steady-state case are presented for the space-frequency domain described by solid displacements and fluid pressure in a homogeneous viscoelastic medium. The effective bulk modulus of a multiphase flow is computed by the Voigt formula, and the characteristic squirt-flow length is revised for the gas-included case. We then build a viscoelastic BISQ model containing a multiphase flow. Through using this model, wave dispersion and attenuation are studied in a medium with low porosity and low permeability. Furthermore, this model is applied to observed interwell seismic data. Analysis of these data reveals that the viscoelastic parameter tan δ is not a constant. Thus, we present a linear frequency-dependent function in the interwell seismic frequency range to express tan δ. This improves the fit between the observed data and theoretical results.