A general method for extracting the amplitude spectrum of the seismic wavelet from the seismic traces

When solving geophysical problems using reflection seismology, extracting the amplitude spectrum of the seismic wavelet (ASSW) from a seismic trace is the basis for many downstream works, such as deconvolution and sparse reflection coefficient inversion. This paper pertains to statistical methods for estimating ASSW, that is, separating the scattering effect of the formation from the amplitude spectrum of a seismic trace to obtain a band-limited ASSW. Common methods assume the reflection coefficient sequence (RCS) is white, making them unsatisfactory in many cases. Gao et al (2017 Inverse Problems 33 085005) proposed an ASSW extraction method based on contraction operator mapping (COM method) and experimentally proved it effective for non-white RCSs. However, this method is only valid for unimodal ASSW, which makes it unsuitable for most sources. We propose a general method for estimating ASSW which does not require the whiteness assumption of the RCS and does not restrict the specific form of ASSW. We show that the COM method has function representation limitations and redefines a new operator, proving that it is also a contractive mapping. Our method can be regarded as a general form of the COM method, filling the theoretical gap that existing methods cannot be applied to non-white RCS and non-unimodal ASSW. It provides a general method for the estimation of ASSW. We thoroughly verify this generality by simulating different source types while considering wavelet attenuation. Compared with the COM method, the proposed method has absolute advantages.