INITIAL-VALUE AND MODAL APPROACHES FOR TRANSIENT VISCOELASTIC RESPONSES WITH COMPLEX VISCOSITY PROFILES

An initial-value theory is proposed for studying viscoelastic response s of compressible earth models with complex viscosity profiles. Contin uous spectra are caused by both compressibility and the viscosity stra tification, and they can cause numerical difficulties for the modal ap proach. We have studied the different responses for various types of v iscosity profiles and found that there are differences in the response s at short wavelengths for viscosity profiles with sharp low-viscosity zones. We found that many modes are required to match the full initia l-value solutions in the presence of sharp viscosity stratifications i n both the upper and lower mantle. The normal-mode approach is best su ited for simple layered models, long wavelengths and timescales greate r than several thousand years, while the initial-value approach is ind ispensable in treating short-timescale problems with sharp low-viscosi ty zones in the upper mantle and viscosity stratification in the lower mantle.