A new approach for extracting the amplitude spectrum of the seismic wavelet from the seismic traces

In reflection seismology, knowing the seismic wavelet is important both for processing seismic data and for modeling the seismic response. There are two approaches to obtain the seismic wavelet. One approach is deterministic and the other is statistic. This work belongs to the second category. A seismic wavelet is determined by the product of amplitude spectrum and phase spectrum. A conventional method uses a two-step procedure to estimate the seismic wavelet. The first step is for the amplitude spectrum, and the second step is for the phase spectrum. So extracting the amplitude spectrum of a seismic wavelet (ASSW) from the amplitude spectrum of a seismic trace is a key step. The commonly used methods are correlation-based method, the log-spectrum-averaging method and spectrum-shaping method. All these methods assume the reflection coefficient sequence is white, which may not be valid under some conditions. In this paper, we propose a new approach to obtain ASSW without the whiteness assumption about reflectivity. We define an operator on a properly chosen function space and prove that the operator is contractive in this space. Then, we convert the problem of estimating the ASSW into one of finding the fixed point of the operator. We give the algorithm in detail based on the J Gao et al Printed in the UK 085005 INPEEY © 2017 IOP Publishing Ltd 33 Inverse Problems