In seismic exploration, statistical wavelet estimation and deconvolution are standard tools. Both of these processes assume randomness in the seismic reflectivity sequence and also make a minimum phase assumption about the actual wavelet embedded in the trace. The validity of these assumptions is examined by using well-log reflectivity sequences, synthetic seismic traces, and by using a procedure for evaluating the resulting deconvolutions. With real data, wavelet estimations are compared with the insitu recording of the actual waveform from a vertical seismic profile (VSP). As a result of these investigations, this thesis presents a fairly simple group of tests that can be used to evaluate the validity of the randomness and minimum phase assumptions. From the investigations of seismic data in Alberta, it is concluded that the assumption of reflectivity randomness is less of a problem in deconvolution than other assumptions such as phase and stationarity.
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