One major cause of elastic wave attenuation in heterogeneous porous media is wave-induced flow of the pore fluid between heterogeneities of various scales. It is believed that for frequencies below 1kHz, the most important cause is the wave-induced flow between mesoscopic inhomogeneities, which are large compared with the typical individual pore size but small compared to the wavelength. Various laboratory experiments in some natural porous materials provide evidence for the presence of centimeter-scale mesoscopic heterogeneities. Laboratory and field measurements of seismic attenuation in fluid-saturated rocks provide indications of the role of the wave-induced flow. Signatures of wave-induced flow include the frequency and saturation dependence of P-wave attenuation and its associated velocity dispersion, frequency-dependent shear-wave splitting, and attenuation anisotropy. During the last four decades, numerous models for attenuation and velocity dispersion from wave-induced flow have been developed with varying degrees of rigor and complexity. These models can be categorized roughly into three groups ac-cording to their underlying theoretical framework. The first group of models is based on Biot's theory of poroelasticity. The second group is based on elastodynamic theory where local fluid flow is incorporated through an additional hydrodynamic equation. Another group of models is derived using the theory of viscoelasticity. Though all models predict attenuation and velocity dispersion typical for a relaxation process, there exist differences that can be related to the type of disorder (periodic, random, space dimension) and to the way the local flow is incorporated. The differences manifest themselves in different asymptotic scaling laws for attenuation and in different expressions for characteristic frequencies. In recent years, some theoretical models of wave-induced fluid flow have been validated numerically, using finite-difference, finite-element, and reflectivity algorithms applied to Biot's equations of poroelasticity. Application of theoretical models to real seismic data requires further studies using broadband laboratory and field measurements of attenuation and dispersion for different rocks as well as development of more robust methods for estimating dissipation attributes from field data.

Lead zirconate titanate (PZT) films with a thickness of more than 10 µm were prepared by the aerosol deposition method and their microstructure and chemical composition were investigated by transmission electron microscopy (TEM) and energy dispersive X-ray spectra (EDX) analysis. A damage layer was observed at the interface between PZT and the Si substrate during the deposition. The microstructure of the as-deposited film at room temperature consisted of randomly oriented small crystallites with sizes of less than 40 nm and large crystallites of 100 nm to 300 nm size, which were observed in the primary powder. The Pb/Ti/Zr ratio along the film stacking direction and around the grain boundaries was almost the same as that observed inside the crystallites and the primary powder with a morphotropic phase boundary composition of (Pb(Zr_0.52Ti_0.48)O₃). The marked improvement of the electrical properties observed in the deposited films after annealing was mainly due to the crystal growth of small crystallites.

Crack-free $[{\mathrm{Pb(Zr}}_{\mathrm{0.52}}{\mathrm{, Ti}}_{\mathrm{0.48}}{\mathrm{)O}}_{\mathrm{3}}]$ (PZT) films with more than 10 μm thickness as the piezoelectric material, were formed on stainless-steel (SUS304) and ${\mathrm{Pt/Ti/SiO}}_{\mathrm{2}}\mathrm{/Si}$ substrates by aerosol deposition and then annealed at 600 °C in air. The deposition rate was 20 μm/min in an area of $\text{5×5\hspace{0.05em}}{\mathrm{mm}}^{\mathrm{2}}.$ To estimate the piezoelectric and mechanical properties of PZT films, a unimorph structured PZT and a free-standing cantilever were fabricated. The Young’s modulus ${\mathrm{(Y}}_{11})$ of the PZT film was 80 GPa. Poling at 40 kV/cm, 250 °C for 20 min increased the properties by a factor of 4.0–5.5, resulting in the piezoelectric coefficient ${\mathrm{(-d}}_{31})$ varying from 80 to 180 pm/V.