Influence of inaccurate wavelet phase estimation on seismic inversion

Abstract

On the assumption that the seismic wavelet amplitude spectrum is estimated accurately, a group of wavelets with different phase spectra, regarded as estimated wavelets, are used to implement linear least-squares inversion. During inversion, except for the wavelet phase, all other factors affecting inversion results are not taken into account. The inversion results of a sparse reflectivity model (or blocky impedance model) show that: (1) although the synthetic data using inversion results matches well with the original seismic data, the inverted reflectivity and acoustic impedance are different from that of the real model. (2) the inversion result reliability is dependent on the estimated wavelet Z transform root distribution. When the estimated wavelet Z transform roots only differ from that of the real wavelet near the unit circle, the inverted reflectivity and impedance are usually consistent with the real model; (3) although the synthetic data matches well with the original data and the Cauchy norm (or modified Cauchy norm) with a constant damping parameter has been optimized, the inverted results are still greatly different from the real model. Finally, we suggest using the L1 norm, Kurtosis, variation, Cauchy norm with adaptive damping parameter or/and modified Cauchy norm with adaptive damping parameter as evaluation criteria to reduce the bad influence of inaccurate wavelet phase estimation and obtain good results in theory.