Strong motion; array data; normal mode; elastic medium; earthquake source; mean square error
The strong motion displacement records available during an earthquake can be treated as the response of the earth as the a structural system to unknown forces acting at unknown locations. Thus, if the part of the earth participating in ground motion is modelled as a known finite elastic medium, one can attempt to model the source location and forces generated during an earthquake as an inverse problem in structural dynamics. Based on this analogy, a simple model for the basic earthquake source is proposed. The unknown source is assumed to be a sequence of impulses acting at locations yet to be found. These unknown impulses and their locations are found using the normal mode expansion along with a minimization of mean square error. The medium is assumed to be finite, elastic, homogeneous, layered and horizontal with a specific set of boundary conditions. Detailed results are obtained for Uttarkashi earthquake. The impulse locations exhibit a linear structure closely associated with the causative fault. The results obtained are shown to be in good agreement with reported values. The proposed engineering model is then used to simulate the acceleration time histories at a few recording stations. The earthquake source in terms of a sequence of impulses acting at different locations is applied on a 2D finite elastic medium and acceleration time histories are found using finite element methods. The synthetic accelerations obtained are in close match with the recorded accelerations.