QUASI-STATIC RESPONSE OF A LAYERED VISCOELASTIC HALF-SPACE TO GENERAL SURFACE LOADING

Analytical solutions to a prestressed, multilayered, elastic half-space subjected to general surface loads are derived using the Cartesian system of vector functions. The solutions are then applied to the Maxwell viscoelastic medium with time-dependent surface loading by means of the correspondence principle and the normal mode method. The number of layers in the model and the pattern of surface load, at least in principle, are unrestrained. This theoretical result is convenient for numerical calculation, and is applicable to the study of postglacial rebound, the inversion of physical parameters of the Earth's interior, the analysis of the evolution of a sedimentary basin, and so forth. As a numerical example, the evolution of the Williston Basin is investigated. The present study differs from an earlier analysis of that basin in two aspects: a four-layered model is taken instead of a two-layered one, and the surface sediment loading is treated as rectangular parallelopipeds with time-dependent heights rather than as a point load. The computed subsidence curves agree quite well with the data from drilling wells.