NEW SCHEMES FOR PROCESSING ACCELEROGRAMS

Abstract

Strong ground motion data is the primary input for earthquake response analysis and design of structures, equipments and other life line systems. The best description of strong earthquakes is provided by accelerographs which produce time history of the three orthogonal translational components of ground acceleration at the location where it is installed. It is, therefore, essential that the information is extracted as accuarately as possible from accelerograph records (known as accelerograms) and this be interpreted carefully. In work presented herein, studies have been carried out on various aspects ofpro cessing and interpretation of strong motion data including survey of literature available on the subject. The work done by different investigators is reviewed to understand the causes and characteristics of the noise and other transformations in the records. About a dozen schemes are discussed for correction of data obtained from accelerographs. Lit erature related to characteristics of digital accelerographs and correction schemes for their records is also reviewed. Based on this literature survey, gaps and shortcomings are identified in the prevailing practices of strong motion data processing. In the present work an attempt is made to fill these gaps and find solutions for some of these problems. For RESA V which is an analog accelerograph developed in India, detailed noise characteristics have not been studied. This has been done through a study of straight line traces of RESA V for 10, 20 and 30 seconds duration, digitized by three different operators with each trace being digitized three times by each operator. Fourier transfor mation spectra and velocity response spectra for zero damping for all the 27 digitized records of noise are determined. A comparison with other standard analog accelero graphs indicated that the level of noise present in records of RESA V is more, in low as well as high frequency ranges. This is attributed mainly due to the thickness of trace of RESA V which suggests that the optics of the instrument needs improvement. The average and standard deviation of maximum acceleration, velocity and displacement of noise history of RESA V has also been worked out. The digitized uncorrected accelerograms which are usually available at unequal sample interval (nonuniform samples) are conventionally converted into data with con stant time interval through linear interpolation. It is a well recognized that linear inter polation introduces frequencies from zero to infinity. In the digital data which is ought to be band limited, linear interpolation distorts the entire band upto Nyquist frequency due to effect of aliasing. In the work reported herein, a concept of stable sampling set is presented and guidelines are provided for operators who perform digitizations IV on semi-automatic digitizers. Based on this study, some of the published uncorrected accelerograms are reviewed and limitations of these accelerograms in regard to highest frequency that can be retrieved from such data is pointed out. An iterative algorithm is discussed to recover band limited signal from nonuniform samples. Based on this algorithm, ascheme is developed for band limited interpolation of nonuniform samples of uncorrected accelerogram to obtain the same at a uniform interval of 200 samples per second. Deficiencies in linear interpolation are highlighted through comparison with different types of sequences obtained through band limited interpolation. For several numerical compulsions, it often becomes necessary for the users of corrected accelerogram to reduce its time steps which are generally made available to them at equal intervals of 0.02 second. The prevailing practice, again, is to linearly inter polate the signal to get the desired sampling rate. However, as the original accelerogram is essentially a band limited signal, linear interpolation modifies the frequency contents of the data and introduces spurious high frequency components at the cost of reduc ing power in the low frequency range. This work highlights the inadequacy of linear interpolation of uniform samples and suggests the use of an interpolation technique by virtue of which the band limited property is maintained. To illustrate the usefulness of the scheme, simple structural systems are analysed using both conventional linear interpolation and with the aid of the proposed band limited interpolation technique. With the above background work, a scheme for correction of records obtained from analog accelerograph is developed. The proposed scheme first performs band limited interpolation from nonuniform samples to obtain the uncorrected accelerogram at 200 samples per second. The process of decimation, instrument correction and band pass filtering is done in frequency domain and the scheme controls the frequency contents of the data during the processing. If the data is required at higher sampling rate then band limited interpolation is recommended. The integration to obtain velocity and displacement is also performed in frequency domain. The proposed correction scheme is comapared with three other correction schemes namely those of Lee and Trifunac [56], of Erdik and Kubin [32] and of Khemici and Chi ang [50]. Response of different sections of the four processing schemes with white noise as input is first compared and then comparison of overall response of the schemes to white noise input is done. Advantages of the proposed processing technique is estab lished by comparing it to the ideal case. Illustrative examples are taken by processing four uncorrected accelerograms of different earthquakes by all the four processing tech niques and a comparison in a tabular form is presented. Although it is established that the noise content in the data recordedfrom digital accelerographs is far less than the analog accelerographs yet the record of digital ac celerograph does get transformed at various stages and in the process noise does creep in which suggests that it is essential to understand these transformations and noise so that true signal can be retrieved. In this work transformations of the signal which take place in the accelerometer and anti aliasing filter are studied and their solution presented. In addition to above transformations, the system continuously records instrumen tal or environmental noise. This pre event portion of the record of digital accelerograph represents the characteristics of this noise which is modelled as coloured noise. An adaptive filter is then developed to cancel noise from the recorded event. In the end of the thesis, conclusions of the various aspects of the studies are summarized.