SIMULATION OF MULTIPLE-SCATTERED CODA WAVE EXCITATION BASED ON THE ENERGY-CONSERVATION LAW

The space-time distribution of the energy density of the multiple-scattered coda wave is synthesized for the case of isotropic scattering with no intrinsic absorption, using the Monte Carlo simulation method in the three dimensional space based on the energy conservation law. The partition of the scattered energy into scattering of different orders is studied. A new table of expansion coefficients for the energy density up to 10th-order scattering is presented, for the case where the total travel distance of the scattered wave is much longer than the hypocentral distance. Using the derived coefficients, the interpretation of the coda Q-1 value is discussed. When multiple-scattering effects are considered, the coda Q-1 is not so sensitive to the difference of scattering strength, and is different from the Q-1 value of a direct S wave even if the scattering strength is very weak. Decrease in the coda Q-1 with lapse time cannot be explained by only the multiple-scattering effects. The time integral of the energy density distribution of this simulation is compared with a formula proposed by Wu derived from the radiative transfer theory. The results are consistent with each other; however, the evaluation of the ratio of scattering attenuation to total attenuation based on Wu's formula is strongly affected by the length of lapse time window.