Macroscopic seismic responses of layered linear anelastic solids: Wave-induced internal deformations beyond the viscoelastic model

Abstract

Seismic wave propagation within thinly layered anelastic reservoirs is modeled by direct application of Lagrangian continuum mechanics. Instead of postulating viscoelastic Q-factors or specific microscopic mechanisms, the anelastic properties of the layers are modeled by using generalized macroscopic internal variables. These variables represent averaged measures of various types of internal deformations of the rock, such as relative movements of grains, inclusions, pores and mobile dislocations, wave-induced pore-fluid flows (WIFFs), capillary and layer-boundary effects, or temperature variations. The continuum-mechanics model reveals the existence of body-force (Darcy-type) frictional effects, which are also absent in the viscoelastic model. To implement the attenuation effects observed in laboratory studies, the mechanical properties of the layers are represented by standard linear solid (Zener) rheologies approximating a mesoscopic-scale WIFF effect known as the drained/undrained transition. Optionally, the layer rheologies also include Biot’s poroelastic effects. All compressional- and shear-wave transmission, reflection, and mode-conversion amplitudes and waveforms for primary and secondary waves are modeled at variable angles of incidence. The modeled records exhibit the expected seismic-wave attenuation and dispersion phenomena but differ from the predictions of viscoelastic modeling. The key observation is that wave-propagation effects are sensitive not only to the Q-factors of the layers but also to properties not considered in conventional models: (1) elastic coupling between the internal variables, (2) body-force friction parameters analogous to fluid mobility, and (3) mechanical properties of contact zones between different rocks, such as the effective permeabilities of layer boundaries. Although challenging, these properties of layer boundaries need to be measured for earth’s media and included in the modeling of seismic waves. Another important general observation from this modeling is that the often observed broadband or near-constant seismic Q may result from superposition of the effects of multiple heterogeneities (layers) and material-property contrasts within the medium.