Local Oscillator Model of a Seismic Wave in a Viscoelastic Medium

The work derives a local oscillator model of a seismic wave propagating in an isotropic viscoelastic medium. Wave-propagation equations are formulated for the Maxwell model and the standard linear solid. By locally approximating the spatial dependence of the wavefield, the wave equation is reduced to an ordinary differential equation describing the temporal oscillation observed at a fixed point of the medium. The characteristic equation and its solution are considered, and expressions are obtained for the attenuation, apparent frequency, amplitude, and phase of the local oscillation. Particular cases corresponding to the Maxwell model and to an elastic medium are discussed. Methods are then considered for estimating oscillator parameters from a recorded seismic trace. These include a finite-difference inverse coefficient formulation, the Prony method, the Matrix Pencil method, and nonlinear least-squares estimation using the Levenberg–Marquardt algorithm. The proposed formulation provides a direct connection between the seismic trace recorded at a receiver and the local temporal behavior of a propagating wavefield in a viscoelastic medium. Related materials: Inverse Dynamic Problem in a Viscoelastic Medium. Preprint DOI:https://doi.org/10.5281/zenodo.21723472 Associated model VSP wavefields and inversion results. Dataset DOI:https://doi.org/10.5281/zenodo.21724624