Stochastic Seismic Ground Motion Modelling With Imperfectly Stratified Earth Medium

Abstract

Earthquake wave propagation in an imperfectly stratified linear elastic earth medium, generated by a buried seismic dislocation source, is investigated. Using a first order perturbation approach, it is shown that the total wave field may be obtained as a superposition of a mean wave field and a scattered wave field. Both the mean and the scattered wave fields exist in the same perfectly stratified earth medium, without the presence of the irregular interface. The mean wave field is associated with a buried seismic dislocation source, while the scattered wave field is associated with a set of fictitious discontinuity sources distributed on the fictitious mean interface, which has the same effect as the interface irregularities and can be obtained in terms of the mean wave field. The response in the mean wave field can be obtained using the finite integral transform approach. The response in the scattered wave field may be constructed by the fundamental solution with a sinusoidal interface, which may be obtained using the same approach as the mean wave field. With knowledge of the fundamental solution and its corresponding properties, the statistical properties of the ground motion with an imperfectly stratified earth medium may be evaluated. Finally, a numerical example is carried out for illustration purposes.