Formulation of analytical mechanics for viscous fluid is investigated in order to extend the limits of analytical mechanics to dissipative systems. A procedure to incorporate entropy with a Lagrangian function is performed based on the principle of local thermal equilibrium. Neumann's energy equation in irreversible thermodynamics is applied to derive viscous force from entropy. However, Neumann's energy equation itself is excluded from the Lagrangian function so that it should not explicitly violate time reversal invariance. Heat flow does not concern the equations of motion for fluid. This situation is explained by introducing a new vector field which is the time integral of entropy flow density divided by entropy density into the Lagrangian function. The existence of a new field quantity is regarded acceptable admitting the principle of local thermal equilibrium. The formulation of analytical mechanics for viscous fluid is thus successfully accomplished with the above-mentioned procedure. However, the existence of a new vector field is in the stage of mathematical conjecture. The strict proof of this is left for future study.
Seismic wave attenuation is caused by two major factors, scattering attenuation and intrinsic absorption. A method to separate these two factors from total attenuation is proposed for a case where scattering is isotropic and the random distribution of scatterers and that of absorbers are uniform. The seismic waves recorded at a station from an earthquake can be divided into three portions: a direct wave plus an earlier part of coda waves, a middle part of coda waves and a later part of coda waves. The latter two portions are composed of scattered waves only. The time integral of energy density of each portion is numerically simulated based on the Monte-Carlo method, and is plotted against hypocentral distance. The curves of integrated energy are very sensitive to the seismic albedo which is the ratio of scattering loss to the total attenuation. We offer a set of curves of the integrated energy vs. hypocentral distance for different values of the seismic albedos and different strengths of total attenuation. These curves make it possible to evaluate separately the scattering strength and intrinsic absorption by comparison of the time integrals of actually observed band-pass filtered seismogram's power with the simulated curves.