STRONG MOTION ARRAY DATA AS RESPONSE OF LAYERED ELASTIC MEDIUM

Abstract

Earthquakes generate seismic waves that are manifested as ground motion being recorded by instruments deployed in the field. The ground motion records at near source region, also known as strong ground motion, are of importance in estimating the effects of earthquakes on engineering structures. These records are studied the world over in a variety of ways to estimate possible ground motion due to future earthquakes. Strong ground motion is popularly characterized in terms of a few strong motion parameters. The most popular amongst these parameters has been peak ground acceleration (PGA) and its attenuation pattern. Stochastic modelling of ground motion and generation of standard response spectra have been other important practices in the characterization of earthquakes. With the installation of strong motion arrays (SMA) in seismically active parts of the world, ensembles of strong motion records from the same event are readily available in standard format. These ensembles of records are presently used to understand spatial variability of ground motion, which is of importance in aseismic design of long span structures. However, such studies have been possible at specifically designed arrays where strong motion (SM) data is available at very closely spaced stations. What happens, if the same data is available from arbitrarily located stations at distances ranging from a few kms to hundred kms? How one can benefit from such SM data? Can this data be used to extract some additional information about the earthquake? These are a few questions, the present thesis attempts to answer. Here, the SMA data is interpreted as the response of a layered elastic medium to extract useful information. After a brief state-of-the-art on SM data, analysis, modelling and characterization, the thesis proposes, a novel approach to handle SMA data from arbitrarily located stations and introduces a new strong motion parameter called Force Centre (FC). The strong motion acceleration time histories are discrete point records whereas ground motion is essentially continuous in space. Therefore, the recorded accelerograms are attached with an area weight representing the recording station. The entire region comprising of the recording stations can be thought of as a plane with forces acting in two orthogonal directions at the station locations. It would be interesting to find the point in of application of the resultant of these forces, which is called here Force Centre. To handle the usual scatter present in SMA data, the accelerograms are taken to be gaussian random processes. The FC becomes the ratio of two gaussian random variables at any instant of time. The 2D probability density function (pdf) of ratio of two gaussian random variables is found. The mode of this 2D pdf is called the FC, which is plotted for each one-second interval. The locus of this FC is shown to be closely connected with epicentre and focus. Here the FC has been found for seven sets of SMA data. The analogy of treating the SMA data as coplanar forces leads to a new strong motion parameter namely Force Centre. The novelty of the proposed approach lies in handling all the SMA data together to find the Force Centre. The above rigid body analogy of coplanar forces to analyze SMA data is novel and can be seen as an engineering model for a complex dynamic situation arising during earthquakes. Can this rigid body analogy be improved by bringing in elasticity effects of the medium, is the next question explored in the thesis. For this, the thesis conducts a series of numerical experiments on ID and 2D elastic media to find the input (excitation) knowing the output (displacements). The thesis proposes a methodology for finding the excitation source using the free vibration information and the known surface displacements. The methodology proposed makes use of the normal mode approach of structural dynamics along with principle of minimization of mean square error. It has been shown through numerical experiments that the input (excitation) can be successfully found i.e. its location and magnitude, using the proposed approach. The problem of source determination during earthquakes belongs to the above class of inverse problems where the system and the responses are known but not the excitation. Thus, the question arises whether the methodology proposed earlier can be extended to find earthquake source also. The strong motion records available during an earthquake can be treated as response of earth as 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 earthquake as an inverse problem in structural dynamics. Based on this analogy, the thesis proposes an engineering model for the basic earthquake source. First, the acceleration time histories are double integrated to get SM