WIENER ESTIMATION OF GREEN'S FUNCTION

Abstract

The seismic response of a layered model earth is a convolution of the source time function with impulse response or Green's function of the earth model. This function is the response of the model when an impulse of unit amplitude (defined by a delta function) is sent through the model. To determine the Green's function from recorded seismic data in the presence of noise is an important problem when an estimate of the source time function is available. This is also called signature deconvolution. Among the various techniques that may be used for this purpose, use of Wiener's theory is expected to give acceptable results. The deconvolution first involves estimating the noise in the recorded pulse, removing the same from the data and then applying Wieiiers technique for estimating the Green's function. In this thesis the basic concepts of deconvolution and inverse filtering have been explained. A mathematical approach to wiener filter is also discussed and then its implementation to estimate Green's Cunction. The above method has been demonstrated on a marine seismic data and the findings have been discussed. A numerical experiment has been designed wherein, a synthetic seismogram has been created and noise has been added. An effort has been made to design a filter to minimize the noise for precise deconvolution