Modelling of Seismic-Acoustic Fields in Absorbing Axially Symmetric Mediums with Arbitrary Sources
Based on Biot model, describing the propagation of acoustic disturbances in isotropic porous medium saturated with viscous fluid, and viscoelasticity theory, the modified Biot model is proposed. Viscoelastic behavior in it is given with bulk and shear cementation coefficients, which determine the intergranular interactions. Viscoelastic non-porous medium and viscous fluid are considered as special cases of proposed model. The approximation way of viscoelastic modules is described by the rational functions, allowing their inclusion in our model reducing to calculation of convolutions with exponential kernels. Based on viscoelastic Biot model, the problem statement of acoustic fields’ modeling in axially symmetric case for multipole sources is set up. A method for its solution is presented by azimuthal angle decomposition, which includes the using of nonsplitting perfectly matched layer as boundary transparency conditions. A description of explicit second-order finite-difference scheme on shifted grids, approximating the equations of problem, and an economical method for convolutions’ calculating, which are also included in the transparency conditions, are given. Numerical results of modeling of acoustic laboratory experiment, dipole acoustic logging and seismic exploration are presented, which are compared and analyzed with similar ones obtained from analytical solutions.