Algorithm and code are presented that solve dispersion equations for cylindrically layered media consisting of an arbitrary number of elastic and fluid layers. The algorithm is based on the spectral method which discretizes the underlying wave equations with the help of spectral differentiation matrices and solves the corresponding equations as a generalized eigenvalue problem. For a given frequency the eigenvalues correspond to the wave numbers of different modes. The advantage of this technique is that it is easy to implement, especially for cases where traditional root-finding methods are strongly limited or hard to realize, i.e., for attenuative, anisotropic, and poroelastic media. The application of the new approach is illustrated using models of an elastic cylinder and a fluid-filled tube. The dispersion curves so produced are in good agreement with analytical results, which confirms the accuracy of the method. Particle displacement profiles of the fundamental mode in a free solid cylinder are computed for a range of frequencies.

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S U M M A R YA consistent and unified formulation of Green's functions for wave propagation in poroelastic solids based on Biot's theory is given. Over the last decades various authors have made the attempt to derive different Green's tensor representation for poroelastic solids. Due to the various possible combinations of field variables and source terms the different solutions differ significantly. The main solutions are reviewed and compared. It is shown that these previously reported representations of Green's tensors can be used in a complementary sense such that all possible combinations of field variables and source types are included. As a new element we introduce the concept of moment tensors for poroelasticity. This allows us to describe sources in poroelastic solids in a consistent manner. With the help of the moment tensor concept a pressure source acting on the fluid phase is introduced as well as dipole sources and doublecouple sources. To visualize the results, radiation patterns for all the discussed sources are constructed. The shape of the radiation patterns of the fast compressional and shear wave is the same as in elastodynamics, however, the radiation characteristics of Biot's slow wave are superimposed. The relative magnitudes of the field variables shown in the radiation patterns can be very different for different source types. In particular, for any source acting in the fluid phase the pressure field is dominated by the Biot slow wave having compressional wave polarization.

A new spectral-method algorithm can be used to study wave propagation in cylindrically layered fluid and elastic structures. The cylindrical structure is discretized with Chebyshev points in the radial direction, whereas differentiation matrices are used to approximate the differential operators. We express the problem of determining modal dispersions as a generalized eigenvalue problem that can be solved readily for all eigenvalues corresponding to various axial wavenumbers. Modal dispersions of guided modes can then be expressed in terms of axial wavenumbers as a function of frequency. The associated eigenvectors are related to the displacement potentials that can be used to calculate radial distributions of modal amplitudes as well as stress components at a given frequency. The workflow includes input parameters and the construction of differentiation matrices and boundary conditions that yield the generalized eigenvalue problem. Results from this algorithm for a fluid-filled borehole surrounded by an elastic formation agree very well with those from a root-finding search routine. Computational efficiency of the algorithm has been demonstrated on a four-layer completion model used in a hydrocarbon-producing well. Even though the algorithm is numerically unstable at very low frequencies, it produces reliable and accurate results for multilayered cylindrical structures at moderate frequencies that are of interest in estimating formation properties using modal dispersions.